Bachelor of Management Studies (B.M.S.) SEM VI 2019 20 Oct 2019-20 OPERATION 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
4. Q6 Graph papers will be supplied on request
5. Q1 A) Match the right and closely related answer from Column Y with the text term given in Column X. ( Attempt Any 7 questions ) (7)
6. Q1 B) State whether following statements True or False: ( Attempt any 8) 8 marks
7. Q1 One of the areas of application of Operations Research is in Agriculture
8. Q2 A linear programming model consists of only decision variables and constraints
9. Q3 In graphical method of LPP, the optimum value occurs anywhere in feasible region
10. Q4 If the assignment elements are cost elements , then the objective of the optimal assignment is to maximize the cost
11. Q5 In transportation problem, number of basic allocated (or Occupied) cells should be exactly m+ n + that it becomes non-degenerate
12. Q6 Dummy activity does not consume time or resources
13. Q7 The three time estimates employed in PERT are: optimistic time, average expected time, and
14. Q8 In Sequencing, the time taken by each job in changing over from one machine to another is
15. Q9 The row 10, 20] dominates the row [0, 0, 0]
16. Q10 The column [0, —1, —2] dominates the column [0,
17. Q2 A) Use Graphical method to solve the following Linear programming problem Subject to Constraints 8 marks
18. Q2 B) There are 7 different products in a machine shop. Their manufacturing time in Hrs on machines | and 2 are given below. Each of the product must go through two machines and 2 in the order 1-2
    • (i) Find the sequence of Products that minimizes the total elapsed time. 2
    • (ii) Find the Total Elapsed Time for the optimum Sequence. 3
    • (iii) Calculate the idle time for machine 1. (1)
    • (iv) Calculate the idle time for machine 2. (1)
19. Q2 C) ‘BMS Ltd’ prepared a set of interdependent activities for their upcoming project; details of which is given in below table
    • (i) Construct a network diagram, find critical path and project completion time. 3
    • (ii) Tabulate/Calculate Earliest Start and Finish Time, Latest Start and Finish Time and A company is transporting its units from three manufacturing plants P2 and P3 to four distribution centres D3 and D4. The supply and demand of units with unit cost of transportation (in Rs.) and the schedule followed from plants to distribution centres are given below : (The numbers which are in circle indicates number of units transported from plant to distribution centre)
    • (i) Test the solution for optimality 3
    • (ii) If solution is not optimal find optimal solution. 4
20. Q3 A) Following payoff matrix refers to a two player game, player A and player B. Each player has four strategic options Pay Off in Rs
    • (i) Find the Maximin Strategy. Find the Minimax Strategy. (3) 3
    • (iii) What is the value of the Game? (1)
21. Q3 B) There are five jobs (namely 1,2,3,4 and 5), each of which must go through machines A,B and C in the order ABC. Processing Time (in hours) are given below:
    • (i) Find the sequence that minimizes the total elapsed time required to complete the jobs. Calculate the total elapsed time (3) 2
    • (iii) Idle time on Machine A, Machine B and Machine C. 3
22. Q3 Five salesmen are to be assigned to five territories. Base on past performance, the following table shows the annual sales (is Rs. lakh) that can be generated by each salesman in each territory. Find optimum assignment to maximise sales. (7)
23. Q3 D) Use Simplex method to solve the following Linear programming problem Subject to the constraints, 8 marks
24. Q4 A) The table given below has been taken from the solution procedure of a transportation problem, involving minimization of cost (in Rs.)
25. Q1 Show that the above solution is optimal. Find an optimal solution. 3 marks
    • ii) Does the problem have multiple optimal solutions? Give reasons. If multiple solutions exist, then find one more optimal solution. (3) 2
    • iv) Comment upon the managerial significance of multiple optimal solutions 2
26. Q4 B) A company is making a chart to decide the minimum amount of constituents like proteins, vitamins, carbohydrates, fats etc. Which a man needs on daily basis to fulfil his requirement for medical awareness. The choice is to be made from different type of foods (4 types). The yields per unit for different types of foods are explained below in the chart. Formulate the given linear programming problem 5 marks
27. Q4 (C) A Project which is planned using PERT technique has following details of Average Expected Times calculated using the formula, te and the details of standard
    • a) 1) Construct the network diagram of PERT network and find expected completion time of the project. (3) 1i) Calculate and tabulate the Variance of each activity. (2)
    • b) iii) Determine the probability of completing the project in 17 Weeks. 2
    • iv) If there is a huge penalty for exceeding the project completion deadline of two weeks after estimated projected completion time or Critical Path Duration) What is the probability of being penalized? (2)
    • v) Find project completion time for 95% confidence level. 2
    • vi) If the fixed cost of the project is Rs. 4000000 /- and the variable cost is Rs. 20000/- per week. Find the amount the firm should bid under the policy of 95% confidence of completion of the project. (For the purpose of bidding, consider only cost that is break even — no loss and no profit ) (2)
    • vii) If the project manager wants to complete the project with 95% confidence in 19 weeks, by how much time he crash the critical activities? (1) vili) If the head of activity 3 - 5 wants to work overtime so that he can complete this activity in 2 weeks (instead of 3 weeks ), should he be permitted? (1)
28. Q5 A) Define Operations Research. Discuss the advantages and limitations of O.R. 7 marks
    • B) What do you mean by alternative optimal solution in an Assignment? How do you identify alternative solution in an Assignment problem? Further what is the procedure to find that alternative solution? 8
    • C) Answer Any 3 of the following: 15
    • i) Assumptions in LPP
    • ii) Degeneracy in Transportation Principles of Dominance
    • iv) Assumptions in Job Sequencing
    • v) Dummy activity and its use in network analysis Area Under the Standard Normal Distribution

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