Bachelor of Management Studies (B.M.S.) SEM VI 2016 2017 April 2017 OPRATION RESEARCH Question Paper - Mumbai University | munotes

Questions asked in this paper

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1. Q3 Use of non-programmable calculator is allowed and mobile phones are not allowed
2. Q4 Normal distribution table is printed on the last page for reference
3. Q5 Support your answers with diagrams/ illustrations, wherever necessary
4. Q6 Graph paper will be supplied on request
5. Q1 Attempt any two from the following : 7.5
   • a. Solve by simplex method
   • b. ABC Ltd. manufactures two products P and Q. Profit per unit for P and Qis Rs 40 and Rs 80 respectively. 7.5 One unit of P requires 2 machines hours and one unit of Q requires 3 machines hours. Availability of machine hours is 48 Maximum market demand for 15 units and for Q is 10 units. Formulate as LPP and solve by graphical method to obtain maximum total Profit
   • c. Answer the following:
   • i) Explain the use of slack, surplus and artificial variables in simplex method. 2.5
   • ii) Explain what.is redundant constraint in graphical solution with the help of a neat sketch. 2.5
   • iii) Explain the different types of constraints in LPP. 2.5
6. Q2 Attempt any two from the following:
   • a. Acompany has three factories supply of 800, 600 and 1000 units respectively. There are four warehouses W2, with demand of 400, 500, 700 and 800 units respectively. A feasible solution is given below. (With allocations and data) Test the solution for optimality using modified distribution method. 03 ii: ~If the solution is not optimal, find optimal solution by modifying it. 3.5
   • Q.P. Code : 01856
   • b. There are four machines M3and M,. There are five jobs P, Q, R, Sand T. 7.5 Cost of doing each job on each machine is given below hundreds) Machine process Job R and Machine M3 cannot process Job P Find optional assignment of machines and jobs to minimize total cost
   • c. Answer the following:
   • i) Explain the steps involved in solution.of an unbalanced maximization assignment problem. 2.5
   • ii) Explain what is meant by degeneracy in problem and how to resolve it. 2.5
   • iii) Explain why Vogel’s approximation method (VAM) is a better method than North West corner rule (NWCR) to find initial feasible solution of a transportation problem. 2.5
7. Q3 Attempt any two from the following:
   • a. Asmall project consists of following activities
   • i. Draw network diagram and find critical path and project completion tine. 3.5
   • ii. Find earliest and latest starting and finishing times of all activities (EST, EFT, LST, LFT). 04
   • b. Three time estimates are given for each activity of following project
   • i) Tabulate expected time (te) and variance of all activities. 03
   • ii) Draw network diagram and find total project completion time (Critical path). 2.5
   • iii) What be project completion for 90% confidence of completion? 02
   • Q.P. Code : 01856
   • c. Answer the following:
   • i) Explain difference between CPM and PERT. 2.5
   • ii) Explain what is time cost trade off in project crashing. 2.5
   • iii) What are the objectives of project crashing? 2.5
8. Q4 Attempt any two from the following:
   • a. Four strategic alternatives available for countering four states of nature Ni, Nz, N3and Based on the above information:
   • i) Calculate EMV (expected monetary value) for each strategy and find optimal decision. 03
   • ii) Find EPPI (expected payoff with perfect information) and EVPI (expected value of perfect 02
   • iii) Construct regret table and calculate EOL (expected opportunity loss). 2.5
   • b. Following payoff matrix refers to a two player game, player A and player B. Each player has four (Pay off in Rs.)
   • i. Find the Maximin Strategy. 2.5
   • ii. the Minimax Strategy. 2.5 the value of the Game? 2.5
   • c. Five jobs |, V are to be processed on two machines A and B in the order AB
   • i. Find optimal sequence of jobs. 02 ili. Find idle time for each machine. 02
   • Q.P. Code : 01856
9. Q5 A company produces two products A and B. Profit per unit for A and B is Rs 30 and Rs Three resources Mi, utilized. Capacities of M1, M2and 4, 6 and 12 hours respectively Following feasible solution has been obtained by simplex method Based on the solution answer the following questions
   • i. Is this optimal solutions? Justify. 02
   • ii. What is optimal product mix and optimal profit? 02
   • iii. Is there degeneracy in the solution? Justify. 02
   • iv. Is it unique solution or are there multiple optimal solution? Justify. 02 Vv. What are the shadow prices of Mi, M3? 03
   • vi. Which resources are scarce and which are abundant? 02
   • vii. Find percentage utilization of Mp. 02
   • Q.P. Code : 01856 Area Under Standard Normal Distribution

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