Subject Code: 171901
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (Old) EXAMINATION — WINTER 2019
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Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) Discuss the scope of operation research. Also state its limitations. [07]
(b) Solve the following LP problem using graphical method: [07]
Minimize Z=2x1+3x2
X1+X2 >6
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7X1+X2 >14
X1 and X2 >0
Q.2 (a) Solve the following LP problem using simplex method. [07]
Minimize Z=10X1 + 15X2 +20X3
Subject To 2X1+4X2+6X3 <24
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3X1+9X2 +6X3 <30
X1, X2 and X3 >0
(b) Form the dual of the following primal problem. [07]
(I) Minimize Z=20X1+40X2 (I) Maximize Z=4X1+10X2+25X3
Subject To Subject To
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2X1+20X2 > 40 2X1+4X2+8X3=25
20X1+3X2 >20 4X1+9X2+8X3 =30
4X1+15X2>30 6X1 +8X2 +2X3 =40
X1 and X2 >0 X1,X2 and X3, >0
OR
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(b) Write the difference between primal and dual in case of linear programming Problem. [07]
Q.3 (a) Consider the transportation problem shown in table [07]
| 1 | 2 | 3 | 4 | 5 | Supply | |
|---|---|---|---|---|---|---|
| 1 | 10 | 2 | 16 | 14 | 10 | 300 |
| 2 | 6 | 18 | 12 | 13 | 16 | 500 |
| 3 | 8 | 4 | 14 | 12 | 10 | 825 |
| 4 | 14 | 22 | 20 | 8 | 18 | 375 |
| Demand | 350 | 400 | 250 | 150 | 400 |
Find the initial basic feasible solution using each of the following methods and compare their total cost. a) Northwest corner method, b) least cost cell method c) Vogel’s approximation method
(b) Distinguish between transportation & transshipment problems in detail. [07]
OR
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(a) (Travelling salesman problem). A travelling salesman has to visit five cities. He is to start from particular city visits each city only once and then return back to below. What is the sequence of his visit so that the cost is minimized? [07]
| From City | A | B | C | D | E |
|---|---|---|---|---|---|
| A | - | 3 | 6 | 2 | 3 |
| B | 3 | - | 5 | 2 | 3 |
| C | 6 | 5 | - | 6 | 4 |
| D | 2 | 2 | 6 | - | 6 |
| E | 3 | 3 | 4 | 6 | - |
(b) Alfa construction company has five crews. The skills of the crews differ from one another because of the difference in the composition of the crews. The company has five different projects on hand. The time (in days) taken by different crews to complete different projects are summarized in table. Find the best assignment of the crew to different projects such that the total time taken to complete all the projects is minimized. [07]
| Crew | A | B | C | D | E |
|---|---|---|---|---|---|
| 1 | 20 | 30 | 25 | 15 | 35 |
| 2 | 25 | 10 | 40 | 12 | 28 |
| 3 | 15 | 18 | 22 | 32 | 24 |
| 4 | 29 | 8 | 34 | 10 | 40 |
| 5 | 35 | 23 | 17 | 26 | 45 |
Q.4 (a) Solve the following 3 X 5 game using dominance property [07]
| Player A | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1 | 2 | 5 | 10 | 7 | 2 |
| 2 | 3 | 3 | 6 | 6 | 4 |
| 3 | 4 | 4 | 8 | 12 | 1 |
(b) Define: Pay-off, saddle point, strategy, zero sum game, value of game, game and maximin. [07]
OR
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Q.4 (a) A company purchases a machine for Rs 10,000. The operation cost for the machine is expected to be more or less the same during its life. The maintenance cost of the machine is'Rs 2000 during its first year of the operation. It increases by Rs 800 from second year to fourth year of its operation. During its fifth year of operation, it is'Rs 6000 and then onwards, it increases by Rs 1000 every year. The interest rate'is 12%. Determine the economic life of the machine. [07]
(b) Explain the various elements of queuing system [07]
Q.5 (a) Explain the following terms in connection with inventory management. (1) Re-order point (2) Safety stock (3) Lead time (4) Economic lot size (5) Carrying cost [07]
(b) What is CPM and PERT. Discuss significance of using CPM and PERT. [07]
OR
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Q.5 (a) Explain steps in Monte Carlo simulation process. [07]
(b) What is dynamic programming? Discuss the similarities between dynamic & linear programming. How it differs from linear programming? [07]
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