# 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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