TYBMS Sem 6 Operation Research Question Paper 2026 - Mumbai University | munotes

Questions asked in this paper

• 2. Figures to the right indicate full marks

1. Q3 Use non--programmable calculator is allowed
2. Q4 Normal distribution table is printed on the last page for reference
3. Q5 Support your answers with diagrams
4. Q6 Graph papers will be supplied on request
5. Q1 A) State whether following statements True or False: (Attempt any 8) 8 marks
6. Q1 Operation Research is also termed as Management Science
7. Q2 The objective function is a linear relationship reflecting the objective of an
8. Q3 The feasible region is a convex set
9. Q4 The value of Aj = Cj — Zj row in the simplex table tells us whether the current solution is optimal, and, if it is not, what variable will be in the optimal solution
10. Q5 Ifthe assignment elements are cost elements, then the objective of the optimal assignment is to maximize the cost
11. Q6 MODI method is the best method to get Initial Feasible Transportation solution
12. Q7 The dummy activity has an expected time of zero by definition
13. Q8 The PERT pessimistic time estimate is an estimate of the minimum time an activity
14. Q9 a job sequencing problem, it is assumed that all jobs require the same sequence of operations
15. Q10 If saddle point is available in a game, it is called as pure strategy game
16. Q1 B) Match the right and closely related answer from Column Y with the text term given in Column Attempt Any 7 questions ) (7) equal to total losses of all other waiting or not working
17. Q2 A) M/S. Rajaram Pvt.ltd. and engineering firm has to decide profitable mix for its products i.e. Condenser, Transmitter and Connector with a profit (per 100 units) of %10, %6 and %4 respectively. To produce a shipment of condenser containing 100units required | hour of engineering 10 hours of direct labour and 2 hours of administration service. To produce one shipment of transmitter 1000 units require 1 hour of engineering 5 hours of direct labour and 6 hours of administration, similarly these figures for connectors are 1,4 and 2. There are 100 hours of engineering services available 600 hours of direct labour and 300 hours of administration. What is the most profitable mix find with the help of LPP formulation and From the above information Formulate as LPP (7)
    • B) Find the optimum solution with the help of simplex method 8
18. Q2 C) Five salesmen are to be assigned to five territories. Based on past performance, the followingtable shows the annual sales (is Rs. lakh) that can be generated by each salesman in each territory. Find optimum assignment to maximize sales. (8)
19. Q2 D) Solve by using graphical method Subject to constraints, 7 marks
20. Q3 A) From the data given below
21. Q1 Draw a diagram 2 marks
22. Q3 Crash systematically the activities and determine optimal project duration Indirect Cost is Rs. 70 per day 4 marks
23. Q3 B) You are given a solution for a transportation cost problem. Figures in each cell represent per unit transportation cost. Figures in circle within each cell represent number of units allocated for transportation. and P3 are the 3 Plants and W1, W2 and W3 are the 3 Warehouses. You are required to check the above solution for optimality, if it is not optimal, use MODI method to obtain optimal solution and Find optimal transportation cost
24. Q3 C) A Project which is planned using PERT technique has following details of Average Expected Times calculated using the formula, te = +b 6 and the details of
    • i) Construct the network diagram of PERT network and find expected completion time of the project. (3) 1i) Calculate the Variance of each activity. (4)
    • iii) Determine the probability of completing the project in 21 Weeks. 4
    • iv) If the project manager wants to be 99% certain that the project should be completed on schedule what will be the project duration? (4)
25. Q4 A) You are given the pay-off (profit in matrix in respect of a two person zero-sum game as follows: (7)
    • i. Find the Maximim strategy
    • ii. Find the Minimax strategy What is the Value of the game
26. Q4 B) Six jobs I, II, HI, V and VI are to be processed on two machine A and B in order
    • (i) Find the sequence that minimizes the total elapsed time required to complete the
    • (ii) Calculate the total elapsed time 3
    • (iii) Idle time on for each Machine 3
27. Q4 C) Find the optimal sequence: 8 marks
    • a) Determine the optimum sequence for performing jobs
    • c) Idle time for each machine
28. Q4 (D) you are given the following pay-off matrix of a zero-sum game, determine the optimal strategies for the players and the value of the game. (7)
29. Q5 A) Define Operations Research. Explain limitation of Operation Research. 8 marks
    • B) Explain various cost involved in project crashing. 7
    • C) Write a Short note (Attempt three) 15
    • i) Project crashing
    • ii) | Basis and non-basis variable in simplex table
    • iv) Objectives of critical path Area Under the Standard Normal Distribution

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