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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• 2. Figures to the right indicate full marks

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 paper will be supplied on request
5. Q1 Atempt any two questions :
   • a) Use simplex method to solve the following linear programming problem. (7.5) Subject to constraints
   • b) ABC Ltd. manufactures tables and chairs. They have just acquired a new workshop that can operate 48 hours a week. Production of a table will require 2 hours and a chair will require 3 hours production time. Each table will contribute Rs. 40 to profit while a chair contributes Rs
6. Q80 The marketing department has determined that maximum of 15 tables and 10 chairs can be sold every week. Formulate the linear programming model and determine the optimum product mix of tables and chairs that will maximize profits for the company, by using graphical method of linear programming. (7.5)
   • c) Answer each question in brief :
7. Q1 Discuss the advantages of O.R. (2.5)
   • ii) Explain “feasibility region” in graphical method of Linear Programming. (2.5) ili) Explain the meaning of infeasibility Simplex linear programming
8. Q2 Attempt any two questions :
   • a) A departmental head has four subordinates who differ in efficiency and the tasks differ in their intrinsic difficulty. His estimate of the time each man would take to perform each task is given in the matrix below Time (in hours) How should the tasks be allocated on one to one basis to minimize the total man-hours? Find optimal assignment of men and tasks. (7.5)
   • b) A company produces three models A, B and C of their products in three factories X, Y and Data regarding unit transportation cost in Rs., capacity and demand are given below : Find the optimal allocation of models to the factories and assess the minimum cost by MODI
   • c) Answer each question in brief :
9. Q1 When do we say that an Assignment problem is unbalanced? How do you balance
   • ii) Discuss difference between Assignment and Transportation Problem. (2.5)
   • iii) Degeneracy in a transportation problem. (2.5)
10. Q3 Attempt any two questions :
    • a) Determine EST, EFT, LST, LFT, Trail Event Slack, Head Event Slack in respect of all node points and identify critical path for the following network. The Activity time in days is mentioned on the activities. (7.5) Three time estimates are given for each activity in days of following project
11. Q1 Tabulate expected time (te) and variance of all activities. (2.5)
    • ii) Draw network diagram and find total project completion time. (Critical Path) (2.5) ili) What will be Project completion 90% confidence of completion? (2.5)
    • c) Answer each question in brief :
12. Q1 What is PERT? Explain with examples. (2.5)
    • ii) What are predecessors or preceeding activities? Explain with examples. (2.5) Distinguish between Activity and Event. (2.5)
13. Q4 Attempt any two questions :
    • a) goods company has set up following pay—off table (in Rs. 1000.) for the sales returns of their product. Three strategies $3) are identified to deal with three uncertain States of Nature (Nj, N2, N3) You are required to identify right strategy under following criteria :
    • ii) Maximax. (1)
    • v) Minimax Regret. (2.5)
    • b) There are nine jobs, each of which must go through two machines P and Q in the order PQ, the processing times (in hours) are given below: Find the sequence that minimizes the total elapsed time. Also calculate the idle time for the machines P and Q in this period. (7.5)
    • c) Given the following pay-off matrix of a zero-sum game, determine
14. Q1 The optimal strategy for the player A (2.5)
    • ii) The optimal strategy for the player A (2.5) 1i) The value of the game (2.5)
15. Q5 A business problem is formulated and expressed below as an LPP, X1 & X2 are the product on volumes of products A & B respectively. The resources required for producing these products are & R2. Total profit is Z Subject to the resource constaints, Simplex algorithm of LPP, applied to the above problem yielded the following feasible solution
    • a) Please improve the above solution to optimality. 5
    • b) Study the solution found by you and answer the following questions with justification
16. Q1 Is the solution found by you infeasible? Is this a case of multiple optimal solutions (alternate optima)? (2) What is the product mix and the maximum profit? (2) 2 marks
    • iv) Calculate the percent utilization of resources & R2. 2
    • v) If one unit of R2 becomes unavailable what is the reduction in maximum profit? Area Under Standard Normal Distribution 2

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