GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- VII (New) EXAMINATION — WINTER 2019
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Subject Code: 2171901 Date: 28/11/2019
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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| MARKS | |||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Q.1 (a) Define Operations research. Explain any two area of feasible application of OR in your college. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Briefly explain: Phases of Operation Research. | 04 | ||||||||||||||||||||||||||||||||||||
(c) Tom has received certain amount as will from his maternal parents. He is contemplating how much money he should invest in various alternatives open to him so as to maximize return on investment. The investment alternatives are given below with his subjective estimate of the risk involved on a five — point scale. He decided that the risk should not be more than 4 and the fund should not be locked up for more than 15 years. He would necessarily invest at least 25% in house construction. Formulate the LPP:
| 07 | ||||||||||||||||||||||||||||||||||||
| Q.2 (a) What are the characteristics of Linear Programming Problems? Discuss. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Solve problem using graphical method: Max Z =20 x1:+30 x2 --- Content provided by FirstRanker.com --- Subject to 2x1 + 3x2 > 120x1+ x2<40 2x1 + 1.5x2>90 X1, X2>0 | 04 | ||||||||||||||||||||||||||||||||||||
| (c) Solve the following problem using simplex method: Minimize Z = x1 — 3x2 + 2X3 --- Content provided by FirstRanker.com --- Subject to 3x1 —x2 +2x3< 72x1 +4x2 +2x3< 12 4x1 +3x2+8x3< 10 X1, X2, X3 >0 | 07 | ||||||||||||||||||||||||||||||||||||
| OR | |||||||||||||||||||||||||||||||||||||
| (c) Solve the following dual problem: Max Z=40x; + 50 x» --- Content provided by FirstRanker.com --- Subject to 2x1 +3x2< 38x1+4x2<5 X1, X2>0 Also, find out the result of primal from final table of dual. | 07 | ||||||||||||||||||||||||||||||||||||
| Q.3 (a) How profit maximization problem can be solved by assignment Problem? | 03 | ||||||||||||||||||||||||||||||||||||
| (b) A bank has only one cashier. Cashier working style follows Poisson distribution with mean service rate of 8 customer per hour. The customer arrives at a rate of 5 per hour during entire 8 hours. Find out: 1. Equipment utilization --- Content provided by FirstRanker.com --- 1l. The percentage time that an arriving customer has to wait.1il. Average system time. | 04 | ||||||||||||||||||||||||||||||||||||
(c) Solve the minimal assignment problem whose matrix as follows: Also find the other optimal solution, if any.
| 07 | ||||||||||||||||||||||||||||||||||||
| OR | |||||||||||||||||||||||||||||||||||||
| Q.3 (a) How to tackle the non-square matrix in the assignment problem? Explain with suitable example. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Explain: Kendell’s Notation in terms of Queuing Theory | 04 | ||||||||||||||||||||||||||||||||||||
(c) Find out the optimum transportation cost based on given table:
| 07 | ||||||||||||||||||||||||||||||||||||
| Q.4 (a) Explain: Procedure for Group Replacement Theory | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Derive the equation for Economic Order Quantity (EOQ) for constant demand with the condition of no shortage. | 04 | ||||||||||||||||||||||||||||||||||||
(c) The initial price of an equilibrium is Rs. 5000. The running cost varies as below:
--- Content provided by FirstRanker.com --- Taking a discount rate of 0.90, find out the optimum replacement interval. | 07 | ||||||||||||||||||||||||||||||||||||
| OR | |||||||||||||||||||||||||||||||||||||
| Q.4 (a) Discuss different types of costs associated with inventory. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Explain: ABC analysis and its importance. | 04 | ||||||||||||||||||||||||||||||||||||
(c) Solve the following game.
| 07 | ||||||||||||||||||||||||||||||||||||
| Q.5 (a) Explain the concept of ‘Expected Value of Perfect Information’ in context of Decision theory. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Differentiate: PERT and CPM. | 04 | ||||||||||||||||||||||||||||||||||||
(c) XYZ company is currently working with a process which fetches profit of Rs. 12000. The following alternatives are available to the company:
--- Content provided by FirstRanker.com --- | 07 | ||||||||||||||||||||||||||||||||||||
| OR | |||||||||||||||||||||||||||||||||||||
| Q.5 (a) Discuss the conditions under which crashing of project is necessary. Also discuss its effect on the project cost. | 03 | ||||||||||||||||||||||||||||||||||||
| (b) Explain steps for decision theory approach. | 04 | ||||||||||||||||||||||||||||||||||||
(c) A small project is composed of following activities whose time estimates are listed below:
(a) Draw the project network. (b) Find the expected duration and variance of each activity. (c) Calculate early and late occurrence of each event. | 07 | ||||||||||||||||||||||||||||||||||||
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