LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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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
Answer ALL the following: (10X2=20)
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
following tasks on two machines:
| 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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