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

Principal buyers                                   20%                            15%                   8%

Cost per advertisement(Rs.)                 8000                            6000                  5000

————————————————————————————————————

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

already decided that magazine A should have no more than 15 advertisements and that

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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