## Loyola College B.Sc. Statistics April 2007 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc.

 LO 19

DEGREE EXAMINATION –STATISTICS

THIRD SEMESTER – APRIL 2007

ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

Date & Time: 02/05/2007 / 9:00 – 12:00        Dept. No.                                                     Max. : 100 Marks

# PART – A

Answer all the questions.                                                           (10 x 2 = 20 Marks)

1. What is the need for an artificial variable in a linear programming problem?
2. How many basic solutions can be obtained for a system of 3 equations with 5 variables?
3. Explain the need for a transportation problem.
4. Express assignment problem as a linear programming problem.
5. What is the objective of a sequencing problem?
6. When an activity is called critical in a project?
7. Distinguish between CPM and PERT.
8. Define holding cost and shortage cost in an inventory model.
9. Write the formula for EOQ in a single item static model explaining the notations used.
10. What are the assumptions in a single item static model?

# PART – B

Answer any five questions.                                                        (5 x 8 = 40 Marks)

1. Nerolac produces both interior and exterior paints from 2 raw materials R1 and R2. The following data provides the basic data of the problem:

Tons of raw material               Maximum availability

per ton

Interior                    Exterior

Raw material, R1                         6                  4                                  24

Raw material, R2                         1                  2                                    6

Profit per ton in 000’s                 5                  4

A market survey indicates that the daily demand for interior paint cannot exceed that of exterior paint by more than 1 ton.  Also, the maximum daily demand of interior paint is 2 tons.

Nerolac wants to find the optimum product mix of interior and exterior paints that maximizes the total daily profit.

Formulate the problem as a linear programming problem.

1. Solve the following linear programming problem graphically.

Max     Z  =  4 x1 + 3 x2

Subject to

2x1 + x2 £ 1000

x1+ x2 £  800

x1 £ 400

x£ 700

x1, x2  ³ 0

1. Obtain the initial basic feasible solution to the following transportation problem using least cost method.

Distribution Centre                                         Availability

W                    X                     Y                     Z

A    20                    25                    50                    12             450

Factory     B    45                    50                    15                    40             500

C     22                   10                    45                    45             550

Requirement    500                  400                  300                  300

1. Four operators are to be assigned to 4 jobs in a company. The time needed by the operators for the jobs are given below.  How should the jobs be assigned so that the time is minimised?

Operators

A         B         C         D

I           15        13        14        17

II         11        12        15        13

Jobs

III        18        12        10        11

IV        15        17        14        16

1. A book binder has one printing press, one binding machine and the manuscripts of a number of different books. The time required to perform the printing and binding operations for each book are known.  Determine the order in which the books should be processed in order to minmise the total time required to process all the books.  Find also the total time required.

Processing time

1         2         3         4         5

Printing time               40        90        80        60        50

Binding time               50        60        20        30        40

1. Draw the network for the data given below and compute the critical path.

Activity                     Predecessor             Time (weeks)

A                                 ¾                                3

B                                 ¾                                5

C                                 ¾                                4

D                                 A                                 2

E                                  B                                 3

F                                  C                                 9

G                                 D, E                             8

H                                 B                                 7

I                                   H, F                             9

1. Find the optimum order quantity for a product for which the price breaks are as

follows

Quantity                                  Unit cost (Rs.)

0 £ y <500                                    10

500 £ y                                         9.25

The monthly demand for the product is 200 units, the cost of storage is 2% of the unit cost and the cost of ordering is Rs.350.

1. Discuss in detail the factors affecting inventory control.

# PART – C

Answer any Two questions.                                                       (2 x 20 = 40 Marks)

1. Use simplex method to solve

Max Z  =  2x1  +  3x2  subject to

x1 + x£  4,   – x1  +  x2  £ 1,  x1  +  2x2  £  5

x1,  x2  ³  0

1. A company has 3 factors A, B, C and four distributors W, X, Y and Z. The monthly production capacity and demand for the distribution centers and the unit transportation costs are given below.

Distribution center                   Availability

W        X        Y        Z

Factory      A         20        25        50        10                    4500

B         45        50        15        40                    5000

C         22        10        45        35                    5500

Demand              5000    4000    3000    3000

1. A project consists of activities A, B, C, _ _ _ _ H, I. Construct the network diagram for the following constraints.

A < D;  A < E;  B < F;  C < G;  D < H:  E, F < I

The project has the following time estimates (in days).

Task                             A         B        C        D        E         F          G         H         I

Optimistic time           5         18        26        16        15        6         7          7          3

Pessimistic time           10        22        40        20        25        12        12        9          5

Most likely time          8         20        33        18        20        9         10        8         4

Obtain the expected times and their variances.  Also obtain the critical path and total float, free float for the activities.

1. a) Explain a single item static model with no shortages in detail.
2. b) An oil manufacturer purchases lubricants at the rate of Rs.42 per piece from a vendor. The requirement of these lubricants is 1800 per year. What should be the order quantity per order, if the cost per placement of an order is Rs.16 and inventory carrying charge per piece per year is only 20 paise?

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## Loyola College B.Sc. Statistics April 2008 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

# NO 6

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2008

# ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES

Date : 07/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions.                         10×2 =  20 marks

1.Define operations research.

2.Explain the need for slack and surplus variables in an LPP.

3.Define basic solution for an LPP.

4.State the objective of  a  transportation  problem.

5.Express an assignment problem as an LPP.

6.Distinquish between CPM and PERT.

7.When is an activity in a network analysis called critical ?

8.Define degenerate solution  for a transportation problem.

9.What  is time horizon and lead time in inventory ?

10 Write a short   note on setup  and  shortage costs.

SECTION –B

Answer any five questions.                         5×8 = 40 marks

11.Obtain all the basic solutions to the following system of linear equations:

2x1 + x2 – x3 = 2

3x1 + 2x2 + x3 = 3.

12.Solve graphically the following LPP:

Max Z = 7x1 + 3x2

Subject to the constraints:

x1 + 2x2    3

x1 + x2     4

x1  5/2

x2  3/2

x10 & x2  0.

13.Find an initial solution for the following transportation problem using least cost

method:

Destination

Origin                    ————————————       Availability

D1        D2     D3      D4

——————————————————————————

O1                           1            2        1         4                        30

O                         3            3        2         1                        50

O3                           4            2        5         9                        20

Requirement         20          40      30       10

——————————————————————————-

14.Six wagons are available at six stations A,B,C,D,E and F. These are required at

stations I,II,III,IV,V and VI. The following table gives the distances(in kilometers)

between various stations:

I           II         III        IV        V         VI

A     20         23        18        10        16        20

B     50         20        17        16        15        11

C     60         30        40        55        8          7

D      6          7          10        20        100      9

E      18         19        28        17        60        70

F       9          10        20        30        40        55

How should the wagons be assigned so that the total distance covered is minimized ?

1. A small maintenance project consists of the following 12 jobs:

Job                         Duration(in days)

• 2

2-3                              7

2-4                               3

3-4                               3

3-5                               5

4-6                               3

5-8                               5

6-7                               8

6-10                             4

7-9                               4

8-9                               1

9-10                             1

(a) Draw the arrow diagram of the project.

(b) Determine the critical path and the project duration.

1. Use simplex method to solve the following LPP:

Max Z = 3x1 + 2x2

Subject to the constraints:

x1+ x2   4

x1 – x2   2

x10, x20

1. Explain the inventory control of a system.
2. Derive a single item static model with the necessary diagram.

SECTION-C

Answer any two questions.                    2×20 = 40 marks

1. Use big M method to

Min Z = 4x1+ 3x2

Subject to the constraints:

2x1 + x2  10

-3x1 +2x2 6

x1 + x2  6

x10,x20

1. Consider the following transportation table showing production and transportation

costs , along with the supply and demand positions of factories/distribution centres:

M1                 M2                   M3                   M4                   Supply

——————————————————————————-

F1                          4                    6                      8                       13                   500

F2                        13                    11                    10                    8                     700

F3                        14                    4                      10                    13                   300

F4                         9                     11                    13                    3                     500

——————————————————————————–

Demand               250                 350                  1050                200

(a) Obtain an initial basic feasible solution by using VAM.

(b) Find the optimal solution for the above given problem.

1. A project is composed of eleven activities ,the time estimates for which are given below:

——————————————————————————————————-

Activity                 optimistic time              normal time                        pessimistic time

(days)                           (days)                                    (days)

——————————————————————————————————–

1-2                                  7                                     9                                              17

1-3                                  10                                   20                                            60

1-4                                  5                                     10                                            15

2-5                                  50                                   65                                            110

2-6                                  30                                   40                                            50

3-6                                  50                                   55                                            90

3-7                                   1                                    5                                              9

4-7                                  40                                   48                                            68

5-8                                  5                                     10                                            15

6-8                                  20                                   27                                            52

7-8                                  30                                   40                                            50

(a) Draw the network diagram for the project.

(b) Find mean and variance of the activities.

(c) Determine the critical path.

(d) What is the probability of completing the project in 125 days ?

22.(a) Derive the single item static model with one price break with the necessary diagrams.

(b) LubeCar specializes in fast automobile oil change.The garage buys car oil in bulk

at \$3 per gallon.A price discount of \$2.50  per gallon is available if LubeCar

purchases more than 1000 gallons.The garage services approximately 150 cars per

day,and each oil change requires 1.25 gallons. LubeCar stores bulk oil at the cost

of \$0.02 per gallon per day.Also the cost of placing an order for bulk oil is

\$20.There is a 2 day lead time for delivery.Determine the optimal inventory policy.

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## Loyola College B.Sc. Computer Science Nov 2006 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

 AK 10

FIFTH SEMESTER – NOV 2006

# CS 5503 – RESOURCE MANAGEMENT TECHNIQUES

(Also equivalent to CSC 509)

Date & Time : 30-10-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer ALL the questions.                                                                                        (10 x 2 = 20)

1. Define Basic Variables.
2. Define an optimal solution.
3. Find the Dual for the following

Maximize

Subject to

1. Write down the route condition for the traveling salesman problem.
2. Define total elapsed time and idle time.
3. Explain planning and scheduling.
4. Define critical path and total float.
5. Explain optimistic time estimate.
6. Define shortage cost and setup cost.
7. Define present worth factor.

SECTION B

Answer ALL the questions.                                                                         (5 x 8 = 40)

1. (a) A firm produces three products. These products are processed on three different machines. The time required to manufacture one unit of each of the three products and the daily capacity of the three machines are given in the table below:
 Time per unit (minutes) Machine Product 1 Product 2 Product 3 Machine capacity(min/day) M1 2 3 2 440 M2 4 – 3 470 M3 2 5 – 430

It is required to determine the number of units to be manufactured for each product daily. The profit per unit for product 1, 2, and 3 is Rs.4, Rs.3, and Rs.6 respectively. It is assumed that all the amount produced are consumed in the market. Formulate the mathematical model for the problem and find it’s dual.

(or)

(b)Solve the following LPP by graphical method

Maximize

Subject to

1. (a) The owner of a small machine shop has four mechanics available to assign jobs for the day. Five jobs are offered with expected profit for each mechanic on each job which are as follows:

Job

 Mechanic A B C D E 1 62 78 50 101 82 2 71 84 61 73 59 3 87 92 111 71 81 4 48 64 87 77 80

Find by using the assignment method, the assignment of mechanics to the job that will result in a maximum profit. Which job should be declined?

(or)

(b) (i) Write the algorithm for processing n jobs on 3 machines.

(ii) Find the sequence that minimizes the total elapsed time required to complete the following task on the machines in the order 1-2-3. Find also the minimum total elapsed time (hrs) and the idle time on the machines.

 Task A B C D E F G Machine 1 3 8 7 4 9 8 7 Machine 2 4 3 2 5 1 4 3 Machine 3 6 7 5 11 5 6 12

1. (a) Construct the network for the project whose activities are given below and compute the total, free and independent float for each activity and hence determine the critical path and the project duration.
 Activity 1-2 1-3 1-5 2-3 2-4 3-4 3-5 3-6 4-6 5-6 Duration (days) 8 7 12 4 10 3 5 10 7 4

(or)

(b)  The following table shows the job of a network along with their time estimates.

 Job 1-2 1-6 2-3 2-4 3-5 4-5 5-8 6-7 7-8 t0 1 2 2 2 7 5 3 5 8 tm 7 5 14 5 10 5 3 8 17 tp 13 14 26 8 19 17 9 29 32

Draw the project network and find the probability that the project is completed in 40 days. [given that].

1. (a) The following time cost applies to a project. Use it to arrive at the network associated with completing the project in the minimum time at minimum cost.
 Normal                Crash Activity Time (days) Cost (Rs) Time (days) Cost (Rs) 1-2 2 800 1 1400 1-3 5 1000 2 2000 1-4 5 1000 3 1800 2-4 1 500 1 500 2-5 5 1500 3 2100 3-4 4 2000 3 3000 3-5 6 1200 4 1600 4-5 3 900 2 1600

(or)

(b)  (i) The demand for an item is 12,000 per year and shortages are allowed. If the unit cost is Rs. 15 and the holding cost is Rs. 20 per year per unit. Determine the optimum total yearly cost. The cost of placing one order is Rs. 6000 and the cost of one shortage is Rs. 100 per year (ii) Define lot-size inventories.

1. (a) (i) A newspaper boy buys paper for 30 paise each and sells them for 70 paise. He cannot return unsold newspaper. Daily demand has the following distribution.
 No of customers 23 24 25 26 27 28 29 30 31 32 Probability 0.01 0.03 0.06 0.1 0.2 0.25 0.15 0.1 0.05 0.05

If each boys demand is independent of the previous days how many papers should he order each day?

(ii) State the reasons for maintaining inventory.

(or)

(b) Let the value of the money be 10% per year and suppose that machine A is replaced after every 3 years whereas machine B is replaced after every 6 years. The yearly cost of both machines is given as under:

 Age 1 2 3 4 5 6 Machine A 1000 200 400 1000 200 400 Machine B 1700 100 200 300 400 500

Determine which machine should be purchased?

SECTION C

Answer any TWO questions.                                                                       (2 x 20 = 40)

1. (a) Use simplex method to solve the LPP

Maximize

Subject to

(b)  Find the optimal solution for the following transportation problem using Modi method.                                               Destination

 1 2 3 4 Supply 1 14 56 48 27 70 2 82 35 21 81 47 3 99 31 71 63 93 Demand 70 35 45 60 210

Origin

(10 + 10)

1. (a) We have five jobs, each of which must go through the two machines A and B in the order AB. Processing times in hours are given in the table below.
 Job 1 2 3 4 5 Machine A 3 8 5 7 4 Machine B 4 10 6 5 8

(c) the following data is pertaining to a project with normal time and crash time.

 Normal                Crash Activity Time (hrs) Cost (Rs) Time (hrs) Cost (Rs) 1-2 8 100 6 200 1-3 4 150 2 350 2-4 2 50 1 90 2-5 10 100 5 400 3-4 5 100 1 200 4-5 3 80 1 100

(i)         If the indirect cost is Rs.100 per day find the least cost schedule.

(ii)        What is the minimum duration?                                                    (7 + 13)

1. (a) Define Lead time and Reorder level.

(b) The annual demand for an item is 3200 units. The unit cost is Rs. 6/- and inventory carrying charges 25% per annum. If the cost of one procurement is    Rs. 150/- determine (i) Economic order quality (ii) time between two consecutive orders             (iii) number of order per year (iv) the optimal total cost.

(c) A taxi owner estimates from his past records that the costs per year for operating a taxi whose purchase price when new is Rs. 60,000 are as given below:

 Age 1 2 3 4 5 Operating Cost (Rs) 10,000 12,000 15,000 18,000 20,000

After 5 years, the operating cost is Rs.6000k where k = 6, 7, 8, 9, 10 (k denoting age in years). If the resale value decreases by 10% of purchase price each year, what is the best replacement policy? Cost of the money is zero.                                        (4 + 8 + 8)

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## Loyola College B.Sc. Computer Science April 2007 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc.

 HC 12

DEGREE EXAMINATION –COMPUTER SCIENCE

FIFTH SEMESTER – APRIL 2007

CS 5503RESOURCE MANAGEMENT TECHNIQUES

Date & Time: 30/04/2007 / 1:00 – 4:00          Dept. No.                                                     Max. : 100 Marks

Section A

Answer ALL the questions.                                                                              (10 x 2 = 20)

1. Define feasible solution.
2. What is a slack variable?
3. Define basic variable.
4. Find the Dual for the following

Maximize

Subject to

1. Define immediate predessor and immediate successor.
2. Define critical path and free float.
3. Define total elapsed time.
4. Explain indirect cost with an example.
5. What do you mean by lot-size inventory?
6. Define depreciation value.

Section B

Answer ALL the questions.                                                                                (5 x 8 = 40)

1. (a) A firm manufactures three types of products A, B and C and sells them at a profit of Rs.2 on type A, Rs.3 on type B and Rs.4 on type C. Each product is processed on three machines M1, M2 and M3. Type A requires 1 minute of processing time on M1, 2 minutes on M2 and 1 minute on M3. Type B requires 1 minute on each machine M1, M2 and M3. Type C requires 2 minutes on M1, 1 minute on M2 and 2 minutes on M3. Machine M1 is available for not more than 6 hrs 40 minutes, machine M2 is available for 10 hrs while machine M3 is available for 4 hrs 20 minutes during any working day. Formulate the mathematical model for the problem.

(or)

(b) Apply graphical method to solve LPP.

Maximize

Subject to

1. (a) Find the initial basic feasible solution for the following transportation problem by,

(i) Least Cost method                        (ii) Vogel’s Approximation method.

Distribution Centers

 D1 D2 D3 D4 Availability S1 11 13 17 14 250 S2 16 18 14 10 300 S3 21 24 13 10 400 Demand 200 225 275 250 950

Origin

(or)

(b)  Solve the following travelling salesman problem.

To

 A B C D A – 46 16 40 B 41 – 50 40 C 82 32 – 60 D 40 40 36 –

From

1. (a) Find the sequence that minimizes the total elapsed time required to complete the following task on the machines M1 and M2 in the order M1M2. Find also the minimum total elapsed time (days).
 Task A B C D E F G H I M1 2 5 4 9 6 8 7 5 4 M2 6 8 7 4 3 9 3 8 11

(or)

(b) Write the algorithm for forward pass calculation.

1. (a) A project has the following time schedule:
 Activity Duration (months) 1-2 2 1-3 2 1-4 1 2-5 4 3-6 8 3-7 5 4-6 3 5-8 1 6-9 5 7-8 4 8-9 3

Construct the network and compute

(i) Total float for each activity.

(ii) Critical path and its duration.

(or)

(b) The annual demand for an item is 3200 units. The unit cost is Rs.6/- and inventory carrying charges 25% per annum. If the cost of one procurement is Rs.150/- determine  (i) Economic order quality (ii) time between two consecutive orders (iii) number of order per year (iv) the optimal total cost.

1. (a) The demand for an item is 18,000 units per year. The holding cost per unit time is Rs. 1.20 and the cost of shortage is Rs. 5.00, the production cost is Rs. 400. Assuming that replenishment rate is instantaneous, determine the optimal order quality.

(or)

(b) Let the value of the money be 10% per year and suppose that machine A is replaced after every 3 years whereas machine B is replaced after every 6 years. The yearly cost of both the machines is given as under:

 Age 1 2 3 4 5 6 Machine A 1000 200 400 1000 200 400 Machine B 1700 100 200 300 400 500

Determine which machine should be purchased?

Section C

Answer any TWO questions.                                                                            (2 x 20 = 40)

1. (a) A firm produces an alloy having the following specification,

(i)             Specific gravity £ 0.98

(ii)            Chromium ³ 8%

(iii)           Melting point ³

Raw materials A, B and C having the properties shown in the table can be used to make the alloy.

Raw material

 Property A B C Specific gravity 0.92 0.97 1.04 Chromium 7% 13% 16% Melting point

Cost of the various raw material per unit ton are: Rs.90 for A, Rs.280 for B and Rs.40 for C. Find the proportions in which A, B and C be used to obtain an alloy of desired properties while the cost of raw materials is minimum.

(b) Solve the following by simplex method.

Maximize

Subject to

and then find its dual.                                                                                          (6 + 14)

1. (a) Five workers are available to work with the machines and the respective costs (in rupees) associated with each worker-machine assignment is given below. A sixth machine is available to replace one of the existing machines and the associated costs are also given below:
 Machines Workers M1 M2 M3 M4 M5 M6 W1 12 3 6 – 5 8 W2 4 11 – 5 – 3 W3 8 2 10 9 7 5 W4 – 7 8 6 12 10 W5 5 8 9 4 6 –
• Determine whether the new machine can be accepted?
• Determine also optimal assignment.

(b)We have four jobs of which have to go through the machines M1, M2… M6 in the

order M1, M2… M6. Processing time (in hrs) is given below:

 Machines M1 M2 M3 M4 M5 M6 A 18 8 7 2 10 25 B 17 6 9 6 8 19 C 11 5 8 5 7 15 D 20 4 3 4 8 12

Determine a sequence of these four jobs that minimizes the total elapsed time.

(12 + 8)

1. (a) A small project is composed of seven activities whose time estimates are listed in the table

as follows.

 Activity 1-2 1-3 2-4 2-5 3-5 4-6 5-6 t0 1 1 2 1 2 2 3 tm 1 4 2 1 5 5 6 tp 7 7 8 1 14 8 15

You are required to

• Draw the project network.
• Find the expected duration and variance of each activity.
• Calculate the early and late occurrence for each event and the expected project length.
• Calculate the variance and standard deviation of the project length.

(b) A newspaper boy buys paper for 30 paise each and sells them for 70 paise. He cannot return

unsold newspaper. Daily demand has the following distribution.

 No of customers 23 24 25 26 27 28 29 30 31 32 Probability 0.01 0.03 0.06 0.1 0.2 0.25 0.15 0.1 0.05 0.05

If each boy’s demand is independent of the previous day’s how many papers should he order each day?

(c) The cost of a machine is Rs. 6100 and its scrap value is Rs. 100. The maintenance costs

found from experience are as follows:

 Year 1 2 3 4 5 6 7 8 Main cost (Rs) 100 250 400 600 900 1200 1600 2000

When should the machine be replaced?                                            (10 + 4 + 6)

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## Loyola College B.Sc. Computer Science April 2008 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 AK 1

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

FIFTH SEMESTER – APRIL 2008

# CS 5503 – RESOURCE MANAGEMENT TECHNIQUES

Date : 03-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART-A

Answer all the questions:                                                                  (10×2=20 marks)

1. Define a general linear programming problem.
2. Write the dual of the following problem:
1. What is an assignment problem?
2. Define degeneracy in a transportation problem.
3. Define total elapsed time in a sequencing problem.
4. What is meant by ‘activity’ and ‘event’ in network analysis?
5. Explain economic order quantities in inventory problems.
6. What are quantity discounts?
7. Give an example of replacement situation.
8. Define present worth of money in replacement models.

PART-B

Answer all the questions:                                                                  (5×8=40 marks)

1. a) Explain basic solution, basic feasible solution and optimal solution in a linear programming problem.

(OR)

1. b) Use graphical method to solve the linear programming problem:
1. a) Give the mathematical formulation of a transportation problem.

(OR)

1. b) A computer centre has three expert programmers. The centre wants three

application programs to be developed. The computer time in minutes required by

the experts for the application programs is given below. Assign the programmers to the programs in such a way that the total computer time is minimum.

Programs

 Programmers A B C 1 120 100 80 2 80 90 110 3 110 140 120
1. a) Mention the assumptions made in a sequencing problem.

(OR)

1. b) A project schedule has the following characteristics:
 Activity Time (in weeks) Activity Time (in weeks) 1-2 4 5-6 4 1-3 1 5-7 8 2-4 1 6-8 1 3-4 1 7-8 2 3-5 6 8-10 5 4-9 5 9-10 7

1. a) Explain the costs involved in inventory models.

(OR)

1. b) A stockist has ot supply 12,000 units of a product per year to his customer. The

demand is fixed and known and shortages are not allowed. The inventory holding cost is Re 0.20 per unit per month and the ordering cost per order is Rs.350. Determine i) the optimal lot size and ii) the time between the orders.

1. a)  A firm is considering replacement of a machine, whose cost price is Rs.12,200 and the scrap value Rs.200. The running costs are found from experience to be as follows:
 Year: 1 2 3 4 5 6 7 Running cost (Rs.): 200 500 800 1200 1800 2500 3200

When should be the machine be replaced?

(OR)

1. b) The yearly cost of two machines A and B when money value is neglected is

given below. Find their cost patterns if money value is 10% per year and hence find which machine is more economical.

 Year: 1 2 3 Machine A (Rs): 1800 1200 1400 Machine B (Rs): 2800 200 1400

PART-C

Answer any TWO questions                                                            (2×20=40 marks)

1. a) Solve by simplex method:
1. b) Find the sequence that minimises the total time required in performing the following jobs on three machines in the order ABC. Processing times (in hours) are given in the following table:
 Jobs: 1 2 3 4 5 Machine A : 8 10 6 7 11 Machine B : 5 6 2 3 4 Machine C: 4 9 8 6 5
1. a) The following table gives the unit cost matrix with supplies ai, i=1,2,3 and demands bj, j=1,2,3,4. Find the optimal solution to minimise the cost.

Destination

 Source 1 2 3 4 ai 1 8 10 7 6 50 2 12 9 4 7 40 3 9 11 10 8 30 bj 25 32 40 23 120
1. b) The time estimates (in months) for the activities of a PERT network are given

below:

 Activity: 1-2 1-3 1-4 2-5 3-5 4-6 5-6 to: 1 1 2 1 2 2 3 tm: 1 4 2 1 5 5 6 tp: 7 7 8 1 14 8 15
1. Draw the network and determine the project length.
2. Calculate the variance of the project.
• Find the probability that the project will be completed in 20 weeks:
1. a) A person is considering to purchase a machine for his factory. The related data about the alternative machines are as follows:
 Machine A Machine B Machine C Present investment (Rs): 1000 12000 15000 Total annual cost (Rs): 2000 1500 1200 Salvage value(Rs): 500 1000 1200 Life (years): 10 10 10

As an advisor of the company, you have been asked to select the best machine considering 12% normal rate of return per year, given, present with factor at 12% for 10 years = 5.65 present worth factor at 12% for 10th year = .322

1. b) The demand for a commodity is 100 units per day. Every time an order is

placed, a fixed cost of Rs.400 is incurred. Holding cost is Re .08 per unit per day.

If the lead time is 13 days, determine the economic lot size and the reorder point.

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## Loyola College B.Sc. Computer Science Nov 2008 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

# NA 14

FIFTH SEMESTER – November 2008

# CS 5503 – RESOURCE MANAGEMENT TECHNIQUES

Date : 10-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A   ( 10 x 2 = 20 Marks)

1. Discuss the slack and surplus variables.
2. What are basic feasible solution and the unbounded solution?
3. Write the dual of the following LPP.

Minimize : z = 3x + 2y

Subject to :     x + y ≥  4;         3x+y ≥20;         x, y ≥ 0.

1. When is an artificial variable introduced in the constraints? Explain with illustration.
2. Obtain the initial solution of the following transportation problem by the north-west corner rule given that (i) the requirements are 40, 90 and 100 units and (ii) the supply are 90, 70  and 70.

 Source Destination S1 S2 S3 D1 15 28 27 D2 24 24 25 D3 22 25 20

1. When is transportation problem said to be unbalanced?  Given an example.
2. What does PERT stand for? What is the objective of PERT?
3. State job sequencing problem.
4. What are reorder level and reorder point?
5. What are the three replacement policies?

SECTION – B   ( 5 x 8 = 40 Marks)

1. (a). Solve the following LPP graphically.

Maximize z = 3x1 + 2 x2

Subject to       5x1 +   x2 ≥10

x1 +   x2 ≥6

x1 + 4x2 ≥12

x1 , x2 ≥ 0

(OR)

(b). Show that the LPP given below has unbounded solution.

Maximize z = 2x1 + x2

Subject to     x1 – x2 ≤ 10

2x1 – x2 ≤ 40

x1 , x2 ≥ 0

1. (a). Solve the following transportation problem.

 Destination Origin Requirement A B C D I 7 4 3 4 15 II 3 2 7 5 25 III 4 4 3 7 20 IV 9 7 5 3 40 12 28 35 25 100

(OR)

(b). The following table gives the profit earned by doing certain jobs on different machines.  Only one job is permitted on a machine.  Assign the jobs to the machines so as to maximize the profit.

 Machines Jobs M1 M2 M3 M4 J1 210 84 120 35 J2 180 168 560 105 J3 210 120 168 42 J4 63 84 112 28

1. (a). Draw the network diagram, find the critical path and the Expected project duration for the project details given below.

 Activity 1-2 1-3 1-4 2–4 2-5 3-5 4-5 Optimistic Time 2 3 4 8 6 2 2 Most likely Time 4 4 5 9 8 3 5 Pessimistic Time 5 6 6 11 12 4 7

(OR)

(b). The time required for printing and binding of books on respective machines are given below.  Determine the order in which the jobs to be processed in order to minimize the total time required to complete the job.

 Book 1 2 3 4 5 6 Printing time on machine A 5 7 2 6 3 4 Binding time on machine B 2 5 4 9 1 3

1. (a). The annual demand for an item is 3200 units.  The unit cost is Rs.6 and the inventory carrying cost is 25% per annum.  If the cost of one procurement is Rs. 150, determine (i) economic order quantity (ii) Number of orders per year and (iii) the optimal cost.

(OR)

(b).  A company buys 500 boxes which is a three month supply.  The cost per box is Rs.125 and the ordering cost is Rs.150.  The inventory carrying cost is estimated at 20% of unit value.  (i)  What is the total annual cost of the existing inventory policy?  (ii)  How much money could be saved by employing the economic order quantity?

1. (a). Derive the replacement policy of an item whose maintenance cost increases with time when the money value is not changed, on the assumption the time is continuous.

(OR)

(b). Obtain the replacement policy of an item whose maintenance cost increases with time when the money value is not changed, on the assumption the time is discrete.

SECTION – C   (2x 20 = 40 Marks)

1. Using the simplex method, solve the following problem.

Maximize  z = 2x1 + 3x2

Subject to the constraints

-x1 + 2x2   ≤ 4

x1 +  2x2  ≤ 6

x1 + 3x2   ≤ 9

x1, x2 ≥ 0.

1. The transportation costs of items per unit manufactured by Glass Company from four different locations to four different warehouses are given below.  Find the allocation of items from locations to warehouses in order to minimize the transportation cost.

 Locations of Company Requirement L1 L2 L3 L4 Warehouses W1 20 36 10 28 10 W2 40 20 45 20 4 W3 75 35 45 50 6 W4 30 35 40 25 5 Availability 13 10 6 6

1. Machine X costs Rs.9000. The annual operating costs are Rs.200 for the first year and the increase by Rs.2000 every year.  Determine the best age at which to replace the machine. If the optimum replacement policy is followed, what will be the average yearly cost of owning and operating the machine?  When the machine X is one year old, machine Y is available at the cost of Rs.10000 and the annual operating costs of Y are Rs.400 for the first year and then increases by Rs.800 every year. Is it necessary to replace X by Y? If so, when?

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## Loyola College B.A. Economics April 2006 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

 AC 4

THIRD SEMESTER – APRIL 2006

# ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

(Also equivalent to STA 100)

Date & Time : 02-05-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

PART – A

# Answer all the questions.                                                                              10 ´ 2 = 20

1. Define slack and surplus variables in an LPP.
2. State any two applications of linear programming problem.
3. What is a transportation problem?
4. How to balance an unbalanced transportation problem?
5. What is the need for an assignment problem?
6. Define critical activity.
7. Explain i). Most likely time ii). Optimistic time in network analysis.
8. What is the objective of sequencing problem?
9. Define i). Holding cost, ii). Shortage cost.
10. What is an economic order quantity (EOQ) in inventory control?

# Answer any five questions.                                                                           5 ´ 8 = 40

1. A Company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suiting, shirting’s and woolens yielding a profit of Rs. 2, Rs. 4 and Rs. 3 per meter respectively. One meter of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing, similarly one meter of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minutes in packing, one meter of woolen requires 3 minutes in each department. In a week, total time of each department is 60, 40 and 80 hours for weaving processing and packing respectively.

Formulate the linear programming problem to find the product mix to maximize the profit.

1. Solve graphically.

Max Z = 5x1 + 3x2

Subject to: x1 + 2x2 £ 18

x1 + x2 £ 9

0 £ x2 £ 6

0 £ x1 £ 4

1. Find the starting solution in the following transportation problem by least lost method.
 Origin D1 D2 D3 Supply O1 16 20 12 200 O2 14 8 18 160 O3 26 24 16 90 Demand 180 120 150

1. A department head has 4 subordinate and 4 jobs to be performed. The time taken by each man to complete the job is given below.

#### Men

A 1 2 3 4
B 18 26 17 11
C 13 28 14 26
D 38 19 18 15
E 19 26 24 10

How should the jobs be assigned to minimize the time?

1. In a factory there are six jobs to perform, each of which should go through two machines A and B in the order A, B. the processing timings (hrs) for the jobs are given below.
 Job 1 2 3 4 5 6 Machine A 1 3 8 5 6 3 Machine B 5 6 3 2 2 10

Find the sequence that would minimize the total elapsed time.

1. A small project consists of 7 activities for which the relevant data are given below.
 Activity Preceding Activities Duration A ——— 4 B ——— 7 C ——— 6 D A, B 5 E A, B 7 F C, D, E 6 G C, D, E 5

Draw the arrow diagram and find the critical path.

1. Explain in detail ABC analysis in inventory control.
2. Explain how will you obtain the economic order quantity for a single item static model in inventory control.

# Answer any two questions.                                                               2 ´ 20 = 40

1. Solve the following linear programming problem by simplex method. Maximize Z = 4x1 + 10x2

Subject to 2x1 + x2 £ 50

2x1 + 5x2 £ 100

2x1 + 3x2 £ 90

x1, x2 ³ 0.

1. A manufacturer has distribution centers X, Y and Z. his retail outlets are A, B, C, D and E. the transport cost per unit between each center outlet is given below:
 Retail outlet Distribution Center A B C D E Supply X 55 30 40 50 50 40 Y 35 30 100 45 60 20 Z 40 60 95 35 30 40 Demand 25 10 20 30 15

Find the optimum solution to the given transportation problem.

1. A project consists of eight activities with the following relevant information.
 Activity Immediate predecessor Optimistic time Most likely time Pessimistic time A ——- 1 1 7 B ——- 1 4 7 C ——- 2 2 8 D A 1 1 1 E B 2 5 14 F C 2 5 8 G D, E 3 6 15 H F, G 1 2 3

1. Draw the PERT network
2. Find the expected completion time and variance of each activity.
• Find the total float and free float.
1. What is the probability of completing the project in time?

1. a). Explain the various problems involved in the inventory management.

b). Explain in detail a single item static model with one price break with the necessary diagrams

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## Loyola College B.A. Economics Nov 2006 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034      B.A. DEGREE EXAMINATION – ECONOMICS

 AB 03

THIRD SEMESTER – NOV 2006

# ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

(Also equivalent to STA 100)

Date & Time : 28-10-2006/9.00-12.00      Dept. No.                                                       Max. : 100 Marks

# PART – A

Answer all questions.                                                                 (10 x 2 = 20 Marks)

1. Define slack and surplus variables.
2. Explain linear programming problem.
3. When do you say that a transportation problem is unbalanced? How to make it balanced?
4. Express a transportation problem as a linear programming problem.
5. What is the objective of a sequencing problem?
6. Write any two uses of an assignment problem.
7. State any two differences between CPM and PERT.
8. Define: a) Network             b) Activity
9. What are the components of a cost function in an inventory model?
10. Define: i) Optimistic time            ii) Pessimistic Time

# PART – B

Answer any Five questions.                                                       (5 x 8 = 40 Marks)

1. A firm manufacturers two products A and B on which the profit earned per unit are Rs.3 and Rs.4 respectively. Each product is processed on two machines M1 and M2 product A requires one minute of processing time on M1 and 2 minutes on M2 while B requires one minute on M1 and one minute on M2.  Machine M1 is available for not more them 7 hours and 30 minutes, while machine M2 is available for 10 hours during any working day.  Formulate the problem as a linear programming problem.
2. Find all the basic solutions to the following system of linear equations:

x1 + 2x2 + x3  =  4

2x1 + x2 + 5x3  =  5

1. Obtain the initial basic feasible solution for the following transportation problem using north-west corner method.

D1        D2        D3        D4        D5        D6    Supply

O1        6         4          8         4          9         6         4

O2        6         7          13        6          8         12        5

O3        3         9          4         5          9         13        3

O4        10        7          11        6          11        10        9

Demand          4         4          5          3          2         3

1. Four professors are capable of teaching any one of 4 different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below.  Each professor is assigned only one course.  Determine an assignment schedule so as to minimize the total course preparation time for all courses.

Professor       Subject 1          Subject 2         Subject 3         Subject 4

A                     2                    10                     9                     7

B                     15                    4                      14                    8

C                     13                   14                     16                    11

D                     4                    15                     13                    9

1. Determine the optimal sequences of jobs that minimizes the total elapsed

time based on the following processing time on machines given in

hours and passing is not allowed.

Job

1          2          3         4          5

A    3          8          7         5          2

Machine   B     3          4          2         1          5

C    5          8          10        7          6

1. Draw the network and find the critical path for the project comprising of 9 activities

Activity              A         B         C         D         E          F          G         H         I

Immediate

Predecessor      __        __        __        A         B         C         D, E     B         H, F

Estimated time

(weeks)              3          5          4          2          3          9          8          7          9

1. Explain ABC Analysis in inventory control.

1. Neon lights in a campus are replaced at the rate of 100 units per day. The physical plant orders the neon lights periodically.  It costs Rs.100 to initiate a purchase order.  A neon light kept in storage is estimated to cost about Rs.2 per day.  The lead-time between placing and receiving an order is 12 days.  Determine the optimal inventory policy for ordering the neon lights.

# PART – C

Answer any Two questions.                                                       (2 x 20 = 40 Marks)

1. Use simplex method to

Maximize  Z = 3x1 + 2x2 + 5x3

Subject to

x1 + 2x2 + x3  £ 430

3x1 + 2x3  £  460

x1 + 4x3  £ 420

x1, x2, x3  ³ 0

1. A manufacturer has distribution centers at X, Y and Z. These centers have availability 40, 20 and 40 units respectively of his product.  His retail outlets at A, B, C, D and E requires 25, 10, 20 30 and 15 units respectively.  The transport cost (in rupees) per unit between each centers and outlet is given below.

Retail outlet

Distribution centre         A        B          C       D        E

X                     55        30        40       50        50

Y                     35        30        100      45        60

Z                      40        60        95        35        30

Determine the optimal distribution to minimize the cost of transportation.

1. A project is composed of 11 activities. The time estimates (in days) for which are given below:

Activity           Optimistic time           Pessimistic time           Most likely time

(1, 2)                            7                                 17                                9

(1, 3)                            10                                60                                20

(1, 4)                            5                                 15                                10

(2, 5)                            50                              110                                65

(2, 6)                            30                                50                                40

(3, 6)                            50                                90                                55

(3, 7)                            1                                 9                                 5

(4, 7)                            40                                68                                48

(5, 8)                            5                                 15                                10

(6, 8)                            20                                52                                27

(7, 8)                            30                                50                                40

• Draw the network diagram for the project.
1. Find the expected value and variance for each activity.
• Find the critical path.
1. Find the total float and free float for each activity.
• What is the probability of completing the project in 125 days?
1. Explain in detail a single item static inventory model with one price break with suitable diagrams.

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## Loyola College B.A. Economics Nov 2008 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

# BA 03

B.A. DEGREE EXAMINATION – ECONOMICS

THIRD SEMESTER – November 2008

# ST 3103 / ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

Date : 11-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART-A

1) Define an optimal solution.

2) When do you say that there is no feasible solution in graphical method of solving  L.P.P?

3) What is the need for an artificial variable in a L.P.P?

4) Briefly explain transportation problem.

5) Give an example for an unbalanced assignment problem and state how to make it   balanced.

6) Define a two machines and n jobs sequencing problem.

7) What is meant by idle time in a sequencing problem?

8) Distinguish pessimistic and optimistic time.

9) Define storage cost and setup cost.

10) What are the factors influencing the inventory models?

PART – B

Answer any FIVE of the following:                                                           (5 X 8 = 40)

11(a) Write down the standard form of the general L.P.P.

(b) A firm can produce three types of cloth say A, B, C, three kinds of wool are  required for it, say red

wool, green wool and blue wool. One unit length of type A  cloth needs 2 yards of red and 3 yards of blue wool; One unit length of type B cloth  needs 3 yards of red, 2 yards of green wool and 2 yards of blue wool; One unit  length of type C cloth needs 5 yards of green wool and 4 yards of blue wool. The  firm has only a stock of 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool. It is assumed that the income obtained from one unit length of type A  is Rs. 3, of type B cloth is Rs. 5 and that of type C cloth is Rs.4. Determine how the  firm should use the available material, so as to maximize the total income from the  finished cloth. Formulate the above problem as a L.P.P.    ( 3+5)

12) A company produces two types of a product: A and B. Each product of A type  requires twice as much

labour time as B type. If all the products are of B type only,  the company can produce 500 of these products per day. The market limit daily sales of A and B types are 150 and 250 respectively. Assuming that the profits per product  of A and B types are Rs.8 and Rs.5 respectively. Solve the L.P.P by  graphical method to maximize the profit.

13) Use simplex method to solve the following L.P.P:

Maximize Z = 5x1+ 4x2

subject to the constraints: 4x1+5x2 £ 10

3x1+2x2 £ 9

8x1+3x2 £ 12

x1 , x2 ³ 0 .

14) Obtain the Initial Basic Feasible Solution for the following transportation problem

using North-West corner rule and Least cost method  :

Destination

 Origin Calicut Bangalore Mumbai Pune Availability Cochin 1 2 1 4 30 Chennai 3 3 2 1 50 Hyderabad 4 2 5 9 20 Requirement 20 40 30 10

(4+4)

15) Solve the following assignment problem:

 I II III IV V 1 11 17 8 16 20 2 9 7 12 6 15 3 13 16 15 12 16 4 21 24 17 28 26 5 14 10 12 11 15

16) Find the sequence that minimizes the total elapsed time required to complete the

 Task A B C D E F G H I Machine  I 2 5 4 9 6 8 7 5 4 Machine II 6 8 7 4 3 9 3 8 11

17) A project consists of a series of tasks with the following relationships. With this

notation construct the network diagram having the following constraints:

A < D,E;     B,D <F ;     C<G;      B,G <H;       F,G <I

Find also the minimum time of completion of the project, when the time of

completion of each task is as follows:

 Task A B C D E F G H I Time 23 8 20 16 24 18 19 4 10

18) An electrical appliance manufacturer wishes to know what the economic quantity

should be for a plastic impeller when the following information is available. Plastic

impellers are replaced at the rate of 100 units per day. It costs Rs.100 to initiate a

purchase order. One impeller kept in storage is estimated to cost about Rs.2 per day.

The lead time between placing and receiving an order is 12 days. Determine the

optimal inventory policy for ordering the plastic impellers.

PART – C

Answer any TWO of the following:                                                           (2 X 20 = 40)

19) Use penalty method to

Minimize z = x1 + 4x2

subject to the constraints:

x1 + 3x2 ³ 4000

x1 + 2x2 £ 3500

x1 + 2x2 ³ 2000

x1, x2,  ³ 0.                                                                  (20)

• (a) A departmental stores wishes to purchase the following quantities of dress and

tenders are submitted by 4 different manufactures who undertake to supply more

than the quantities mentioned in the table. The store estimates that its profit per

dress material will vary with the manufactures as shown in the following table:

Dress

 Manufactures A B C D E Availability W 275 350 425 225 150 300 X 300 325 450 175 100 250 Y 250 350 475 200 125 150 Z 325 275 400 250 175 200 Demand 150 100 75 250 200

How should the orders be placed?

(b) We have 4 jobs each of which has to go through the machines Mj, j =1, 2,…6 in the

order M1,M2, .., M6. Processing time is given below:

Machines

 Jobs M1 M2 M3 M4 M5 M6 A 18 8 7 2 10 25 B 17 6 9 6 8 19 C 11 5 8 5 7 15 D 20 4 3 4 8 12

Determine a sequence of these four jobs that minimizes the total elapsed time T.

• (a)Five jobs are to be processed and five machines are available. Any machine can

process any job with the resulting profit as follows:

Machines

 Jobs A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39

What is the maximum profit that may be expected if an optimum assignment is made?

(b) The data for a PERT network is displayed in the table given below. Determine the critical path and

the expected duration of completion of the entire project. Give answers to the following:

(i) What is the probability that the project duration will exceed 60 days?

(ii) What is the chance of completing the project between 45 days and 54 days?

Time duration (days)

 Activity nodes a m b 1-2 2 4 6 1-3 6 6 6 1-4 6 12 24 2-3 2 5 8 2-5 11 14 23 3-4 15 24 45 3-6 3 6 9 4-6 9 15 27 5-6 4 10 16

22) Explain and derive the single static model with price break.                      (20)

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## Loyola College B.A. Economics April 2009 Resource Management Techniques Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

 YB 06

THIRD SEMESTER – April 2009

# ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES

Date & Time: 17/04/2009 / 1:00 – 4:00      Dept. No.                                                        Max. : 100 Marks

SECTION- A

Answer all the questions.                         10 x 2 =  20 marks

1. Write any two applications  of  operations  research.
2. Define basic solution for a linear programming problem.
3. Distinguish between slack and surplus variables.
4. Express a transportation problem as a linear programming problem.
5. Why is assignment problem viewed as a particular case of transportation problem?
6. What is a sequencing problem?

7 . Provide any two differences between PERT and CPM.

1. When is an activity called critical in network analysis?

9 . Write a note on   (i) setup cost    (ii) holding cost.

10 .State the assumptions of  classic EOQ model.

SECTION- B

Answer any five questions                               5 x 8 = 40 marks

11.The owner of  Metro sports wishes to determine how many advertisements to place in

the selected three monthly magazines A,B and C. His objective  is to advertise in such

a way that total exposure to principal buyers of expensive sports good is maximized.

Percentages of readers for each magazine are known. Exposure in any particular

magazine  is the number of advertisements placed multiplied by the number of

principal buyers. The following data may be used .

————————————————————————————————————

Magazine

———————————————————————————————————

A                                  B                        C

Readers                                                1 lakh                          0.6 lakh             0.4 lakh

————————————————————————————————————

The budgeted amount is at most   Rs.1 lakh for the  advertisements . The owner has

B and C each have at least  80 advertisements. Formulate an LP model for the problem.

1. Use the graphical method to solve the following LPP:

Maximize     Z = 2x1 + 3x2

Subject to the constraints:

x1 + x2  ≤  30  ,  x1 -x2 ≥ 0  ,  x2 ≥ 3  ,

0≤ x1≤ 20  and  0 ≤ x2  ≤ 12.

1. Find all the basic feasible solutions of the equations:

2x1 + 6x2 + 2x3 + x4   = 3

6x1 + 4x2 + 4x3 + 6x4 = 2

1. Find an initial basic feasible solution of the following transportation problem using

Vogel’s approximation method:

I                     II                III             IV      Supply

A                  11                   13                17             14        250

B                  16                    18                14             10       300

C                  21                   24                13              10       400

Demand               200                225               275            250

1. Consider the problem of assigning five machines. The assignment costs are given

below :

Machines

Operators                 A                  B                   C                      D                      E

I                        10                 3                   10                      7                        7

II                         5                  9                    7                      11                       9

III                      13                 18                    2                       9                       10

IV                      15                  3                     2                     12                      12

Assign the   operators   to   different machines so that total cost is minimized.

1. Determine the optimal sequence of jobs that minimizes the total elapsed time based

on the following information processing time on machines given in hours and

passing is not allowed .

Job                :      1                   2                        3                         4                       5

Machine A    :      3                   8                        7                         5                       2

Machine B    :      3                   4                        2                         1                       5

Machine C    :      5                   8                        10                       7                       6

Also find the  idle  time  of machines A ,B and C.

1. The following table gives the activities in a construction project and time duration :

Activity                         Preceding activity                     Normal time (days)

1-2                                           –                                                20

1-3                                           –                                                25

2-3                                         1-2                                              10

2-4                                         1-2                                              12

3-4                                    1-3,   2-3                                            5

4-5                                    2-4  , 3-4                                          10

• Draw the activity network of the project .
• Determine the critical path and the project duration.
• Find the total float and free float for each activity.

1. Derive the classic EOQ model clearly stating the assumptions.

SECTION- C

Answer any two questions                                       2 x 20 = 40 marks

1. Use simplex method to

Minimize Z = x1 – 3x2 + 2x3

Subject to

3x1 – x2 + 2x3    ≤ 7

-2x1 – x2 + 2x3    ≤ 12

-4x1 + 3x2 + 8x3  ≤ 10

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 .

1. National oil company (NOC) has three refineries and four depots. Transportation cost

per ton ,capacities and requirements are given below:

________________________________________________________________________

D1             D2            D3          D4        Capacity (tons)

________________________________________________________________________

R1                               5               7               13           10               700

R2                                          8                6               14           13               400

R3                             12              10                9           11               800

Requirement (tons)  200            600             700        400

Determine optimum allocation of output.

1. A project is composed of eleven activities, the time estimates for which are given

Below:

Activity               optimistic time        normal time          pessimistic time

1-2                              7                              9                                  17

1-3                             10                           20                                  60

1-4                              5                            10                                  15

2-5                            50                            65                                110

2-6                            30                            40                                  50

3-6                            50                            55                                  90

3-7                              1                              5                                    9

4-7                            40                            48                                  68

5-8                              5                            10                                  15

6-8                            20                            27                                  52

7-8                            30                            40                                  50

(a) Draw the network diagram for the project.

(b) Calculate total and free floats.

(c) Determine the critical path.

(d) What is the probability of completing the project in 125 days?

1. (a) Derive the classic EOQ model with price break.

(b) Neon lights in an industrial park are replaced at the rate of 100 units per day.

The physical plant orders the neon lights periodically. It costs \$.100 to initiate a

purchase order,  A neon light kept in storage is estimated to cost about \$.0.02 per

day. The lead time between placing and receiving an order is 12 days. Determine

the optimum inventory policy for ordering the neon lights.

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