Subject Code: 2171503
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE- SEMESTER-VII (NEW) EXAMINATION - WINTER 2020Subject Name: Resource Optimization Techniques
Time: 10:30 AM TO 12:30 PM
Date: 25/01/2021
Total Marks: 56
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Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 (a) What do you mean by ‘Resource optimization’? MARKS 03
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(b) State the application of ROT in industrial context. 04(c) Explain various phases of OR to solve any problem of industries for optimum solution. 07
Q.2 (a) Define OR. 03
(b) Discuss the scope of OR in Indian industries. 04
(c) Find an initial basic feasible solution to the following transportation problem using Vogel’s approximation method. 07
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| 1 | 2 | 3 | 4 | Availability | |
| P | 6 | 2 | 4 | 4 | 20 |
| Q | 3 | 4 | 4 | 5 | 25 |
| Origins R | 5 | 3 | 3 | 2 | 30 |
| S | 4 | -1 | 4 | 1 | 30 |
| Requirements | 30 | 25 | 35 | 25 |
Q.3 (a) What is Linear programming? 03
(b) Explain in short: (i) feasible solution, (ii) basic feasible solution. 04
(c) Solve the following LPP. 07
Minimize 10x+6y+2z
Subject to -x+y+z >= 1
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3x+y-z>=2x,y,z>=0
Q.4 (a) State the applications of Linear programming. 03
(b) Explain in short: (1) optimum solution, (i1) non-degenerate feasible solution. 04
(c) Prove that Dual of Dual is a primal. 07
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Minimize z= x1-3x2+2x3,Subject to 3x1-x2+2x3<=7,
-2x1+4x2<=12,
-4x1+3x2+8x3<= 10,
X1,x2,x3>=0.
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Formulate the dual LP.Q.5 (a) What is degeneracy in transportation problem? 03
(b) How will you do optimality test in transportation problem? 04
(c) Solve following transportation problem for minimum transportation cost. Unit shipping costs in Rs. are given as under: 07
| Warehouse | |
| A | 8 |
| B | 6 |
| C | 3 |
| Demand | 15 |
Q.6 (a) State the application of assignment problem. 03
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(b) Explain MODI method. 04(c) Solve the following sequential problem by graphical and arithmetic method: 07
| Job | M | N | O | P | Q | R | S | T |
| Machine-A | 5 | 4 | 21 | 16 | 15 | 10 | 11 | 5 |
| Machine-B | 7 | 10 | 13 | 11 | 20 | 9 | 5 | 21 |
Q.7 (a) Explain ‘Jockeying’ in queuing. 03
(b) Explain the Kendall’s notation to represent a queuing model. 04
(c) Explain the following queuing model ; M/M/1_(8/FCFS). 07
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Given an average arrival rate =10 per hour , average service time = 4 minutes. Calculate the average queue length, waiting and idle time facilities.Q.8 (a) State the application of Game theory? 03
(b) Define and discuss saddle point and zero sum games. 04
(c) Solve the following Game: 07
| Player Y | |||||
| 1 | 2 | 3 | 4 | 5 | |
| Player X | 0 | -8 | -5 | 1 | 2 |
| 1 | 5 | 8 | -4 | 2 | |
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