MS-51 Operation Research

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ASSIGNMENT

Course Code : MS-51

Course Title : Operation Research

1. Solve the following LP problem using SIMPLEX method

MINIMIZE       Z= 5X₁ - 2X₂ +3X₃

Subject to:

                        2X₁ + 2X₂  - X₃  ³  2

                        3X₁ – 4X₂              ≤ 3

                        X₂  + 3X₃               ≤ 5

X₁ , X₂  and X₃  ³ 0

2. a) Write the DUAL of the LP problem given the Problem - 1 and find out the solution of

Dual problem from the final table of simplex (Primal). (b) Discuss the differences between

PRIMAL and DUAL. (C) Explain  the economic interpretation of DUAL variable.

3. a) Discuss the costs associated with queuing system. Explain how you will decide the    

number of counters to be opened at a certain branch of bank.

b) The mean arrival rate to a service centre is 3 per hour. The mean service time is 10

minutes. Assuming Poisson arrival rate and exponential servicing time, determine the  

following.

(i)     Utilization factor of facility   (ii)  Probability of two units in the system. 

(iii) Expected number of units in the queue    (iv) Expected waiting time of customer in the system.

4. a) What is the game in Game Theory? Explain the best strategy on the basis of

MINIMAX criteria of optimality.

b) Solve the following graphically :

                                           B

- 2             0            - 8 - 4           - 5           - 3

A

 

           

5. Write short notes on the following:

(a)    GOAL programming  (b)  Dynamic programming

 (c) Express Transportation Problem as LPP form  (d)  Application of OR in Industry and government.

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