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Posted By: kishore Member Level: Gold Posted Date: 18 May 2008
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2007 Jawaharlal Nehru Technological University M.C.A Computer Aplications OPERATIONS RESEARCH Question paper
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1. Solve the following linear programming problem:
Max. Z = x1 + x2 + 3x3 - x4
Subjected to x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
x1, x2, x3, x4 = 0
2. Use dual simplex method to solve:
Max. Z = -2x1 – x3
Subject to x1 + x2 – x3 = 5
x1 – 2x2 + 4x3 = 8
x1, x2, x3 = 0
3. A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G and H. Monthly plant capacities are 800, 500 and 900 units respectively. Unit transportation costs (in Rs.) are given below:
From/To
D
E
F
G
H
A
5
8
6
6
3
B
4
7
7
6
6
C
8
4
6
6
3
Monthly warehouse requirements are 400, 400, 500, 400 and 800 units respectively. By using Vogel’s approximation method determine an optimum distribution for company, in order to minimize the total transportation cost.
4.a) Explain the theory of dominance in rectangular games.
b) Use dominance property to solve the game:
35496563788798742853????????????
5.a) State the assumptions and derive economic order quantity formula for inventory control.
b) The annual demand of a product is 10,000 units. Each unit costs Rs.100 if quantity ordered is less than 200 units but in case of above, it costs Rs.95/unit. The annual inventory holding cost is 10% of the value of the unit and ordering cost is Rs.5/order. Find economic lot size.
6. A truck owner from his past experience estimated that the maintenance cost per year of a truck whose purchase price is Rs.6,00,000 and the resale value of truck will be as follows:
Year
Maintenance Cost
(Rs.)
Resale Value in
(Rs.)
1
40,000
5,20,000
2
60,000
4,80,000
3
80,000
4,60,000
4
1,00,000
4,20,000
5
1,20,000
3,60,000
6
1,60,000
3,00,000
7
1,80,000
2,40,000
8
2,00,000
2,00,000
Determine at which time it is profitable to replace truck.
7.a) State the conditions under which the problem of processing of jobs through three machines has been solved. Describe the corresponding algorithm.
b) Find the sequence that minimizes the total elapsed time required to complete the following jobs.
Processing time in hours
No. of jobs
1
2
3
4
5
6
Machine A
4
8
3
6
7
5
Machine B
6
3
7
2
8
4
8. A project consists of a series/tasks labeled A, B, C, …., H, I with the following relationships (wAFind also the minimum time of completion of the project, when the time in days 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
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