GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (OLD) EXAMINATION — SUMMER 2019
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Subject Code: 171901 Date: 21/05/2019Subject Name: Operation Research
Time: 02:30 PM TO 05:00 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) What is OR? What are the characteristics and limitation of OR techniques? 07
Q.1 (b) Solve problem by Graphical method: Maximize Z = 3X1 + 4X3; 07
Subjected to: 5X1 + 4X2 < 200; 3Xa + 5X2 < 150; 5X1 + 4X2 > 100; 8Xa +4X2 > 80; X1,X2 > 0
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Q.2 (a) Three grades of coal A, B and C contain phosphorus and ash as impurities. In a 07
particular industrial process, fuel up to 100 ton (maximum) is required which
should contain ash not more than 3% and phosphorous not more than 0.03%. It
is desired to maximize the profit while satisfying these conditions. There is an
unlimited supply of each grade. The percentage of impurities and the profit of
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grades are given below:| Coal | Phosphorous (%) | Ash (%) | Profit (Rs/ton) |
|---|---|---|---|
| A | 0.02 | 3.0 | 12 |
| B | 0.04 | 2.0 | 15 |
| C | 0.03 | 5.0 | 14 |
Find the proportions in which the three grades are used.
Q.2 (b) Explain the concept of degeneracy in Simplex method. How is it resolved? 07
OR
Explain the following with reference to L.P.P. 07
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1. Slack Variable and Surplus Variable2. Entering Variable & Leaving Variable
Q.3 (a) What is degeneracy? How does the problem of degeneracy arise in a 07
transportation problem? How can we deal with this problem?
Q.3 (b) Solve the following assignment problem: 07
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| I | II | III | IV | V | |
| 11 | 17 | 8 | 16 | 20 | |
| 9 | 7 | 12 | 6 | 15 | |
| 13 | 16 | 15 | 12 | 16 | |
| 21 | 24 | 17 | 28 | 26 | |
| 14 | 10 | 12 | 11 | 13 |
OR
What is an unbalanced assignment problem? How is the Hungarian Assignment 07
Method applied in respect of such a problem?
Q.4 (a) Find the basic feasible solution of the following transportation problem by north-west corner rule. 07
| 1 | 2 | 3 | 4 | 5 | Available | |
|---|---|---|---|---|---|---|
| A | 4 | 3 | 1 | 2 | 6 | 80 |
| B | 5 | 2 | 3 | 4 | 5 | 60 |
| C | 3 | 5 | 6 | 3 | 2 | 40 |
| D | 2 | 4 | 4 | 5 | 3 | 20 |
| Required | 60 | 60 | 30 | 40 | 10 |
Q.4 (b) A Branch of bank has only one typist. Since the typing work varies in length the 07
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typing rate is randomly distributed approximating a Poisson distribution withmean service rate of 8 letters type per hour. The letters arrive at a rate of 5 per
hour during the entire 8- hours work day. If the typewriter is valued at Rs. 1.50
per hour, determine:
a) Equipment utilization
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b) The percent time that an arriving letter has to wait.c) Average system time
d) Average cost due to waiting on the part of typewriter i.e. it remaining idle.
Q.5 (a) What is simulation? What are different phases of simulation process? 07
Q.5 (b) Differentiate between deterministic and stochastic simulation models. 07
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ORDerive the EOQ formula Q = v(2C1D / Ch) Where C1 = Ordering cost, D= Uniform 07
demand and Ch = Inventory holding cost.
Q.5 (a) Explain the following : 07
a) Minimax and maximin principals
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b) Two person zero sum game.Q.5 (b) Explain Crashing of network. Why it is required? 07
The maintenance cost and resale value per year of a machine whose purchase
price is Rs. 7000 is given below:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Maintenance cost (Rs.) | 900 | 1200 | 1600 | 2100 | 2800 | 3700 | 4700 | 5900 |
| Resale value (Rs.) | 4000 | 2000 | 1200 | 600 | 500 | 400 | 400 | 400 |
OR
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Define following terms with respect to CPM/PERT : 07a) Event
b) Merge event
c) Burst event,
d) activity
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e) Processor activityf) Successor activity
g) Dummy activity
Give the difference between C.P.M and P.E.R.T
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