Bachelor of Management Studies (B.M.S.) SEM VI 2017 18 April 2017-18 OPERATION RES Question Paper - Mumbai University | munotes

Questions asked in this paper

• Please check whether you have got the right question paper
• 2. Figures to the right indicate full marks

1. Q3 Use of non-programmable calculator is allowed
2. Q4 Normal distribution table is printed on last page
3. Q5 Support answers by diagrams where applicable
4. Q6 Graph paper will be supplied on Request
5. Q1 Attempt any two questions :
   • a) Use Simplex method to solve the following Linear programming problem 75 Subject to the constraints,
   • b) Use Graphical method to solve the following Linear programming problem 7.5 Subject to the constraints,
   • c) Answer each question in brief:
6. Q1 Discuss characteristics of Operations Research. 2.5 li) Explain “Redundant Constraint’ in Graphical Method of LPP. 2.5 Write the Dual for the following Problem. 2.5 Subject to the constraints,
7. Q2 Attempt any two questions:
   • a) Four jobs are to be assigned to four workers on one to one basis. Cost of each assignment is 7.5 given in Rs. Thousands. Find optimal assignment of job and worker to minimize total cost
   • Q.P. Code :31261
   • b) The quantity of different products (in units) produced by the workers per day are givenin the following matrix along with the profit in Rs. Per unit. Formulate a Profit Matrix and find the optimal assignment of workers to product which will maximize the profit Quantity of Products in Units Profit in Rs. Per 4 2 3
   • c) There are 3 Factories A, B, and three Markets X, Y and Z. Supply at the Factories is 60, 80 and 85 units. the market places is 75, 110 and 40 units. The supply and Demand of units with unit cost of Transportation (in Rs.) and the schedule followed from Factories to Markets are given below: (The numbers which are shown in circle indicates number of units transported from Factories to Markets.) (Cost in Rs.)
8. Q1 Test the given solution for optimality and find optimal Transportation lil) Comment upon the managerial significance of alternate/ multiple optimal 01 Attempt any two questions: 3 marks
   • a) project consists of following activities:
   • Q.P. Code :31261
9. Q1 Construct the network diagram and find out critical path and project completion 2.5
   • ii) Calculate Earliest Start Time, Earliest Finish Time, Latest start time and Latest 04 Finish Time for each activity iil) Calculate Tail Slack and Head Slack for non critical activities. Ol
   • b) The data for a PERT network is given in the following table. The project manager has made following calculations of Average Expected Times from Optimistic time, most likely time and pessimistic time for various activities of a project as well respected standard Deviation and the variance values
   • i) Construct the network diagram of PERT network. 25 li) Identify Critical Path and find the expected completion time of the project. 01 ili) Find project completion time for 95% confidence level. 02
   • iv) If the fixed cost of the project is Rs.30, 00,000/- and the variable cost is Rs.20, 000/- 02 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 situation — no loss and no profit)
   • c) Answer each question in brief:
   • i) What are the objectives of project crashing? 1i) Discuss the concept of Dummy Activity. 7. 5 ili) Discuss the difference between an Activity and an Event. 15
10. Q4 Attempt any two questions
    • a) store with a bakery section is faced with the problem of how many cakes to buy order to meet the day’s demand. The departmental store prefers not to sell day-old cakes. Left over cakes are therefore, a complete loss. On the other hand, if a customer desires cake but all of them have been sold, he will buy elsewhere and the sales will be lost The store has therefore, collected information on the past sales based on 100 day period as shown in the table below:
11. Q1 Construct the conditional Pay-off (profit) table. 2.5 it) Calculate Expected Pay-off (profit) using EMV method and suggest best course of 03 What is the optimal number of cakes that should be bought each day? A cake costs Rs.10/- and sells for Rs.15/ Calculate the Expected Value with Perfect Information. (EVPI) 02
    • Q.P. Code :31261
    • 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 products must go through two machines and 2 in the order | -2
12. Q1 Find the optimal sequence of products manufacturing that minimizes the total elapsed 2 marks
    • ii) Find the total Elapsed time for the optimum sequence. 3.5
    • iii) Calculate the idle time for machine 1. 01
    • iv) Calculate the idle time for machine 2. 01
    • c) You are given the Pay-off (profit in Rs.) matrix in respect of a Person Zero — Sum Game as follows:
13. Q1 Find the Maximin strategy li) Find the Minimax strategy 25 What is the Value of the game? 25 25 marks
14. Q5 There are 3 warehouses A,B, C and four market places Supply at the warehouses is 8,9 and 13 units. Demand at the market places is 8, 9,6 and 7 units The following table shows the unit cost data of transportation and a feasible solution to the problem
    • Q.P. Code :31261
15. Q1 Test the given solution for optimality. li) If the given solution is not optimal, find optimal solution using MODI method and 03 calculate optimal cost of transportation From the obtained Optimal Table, answer the following Questions lil) If 3 units are transported from B to P, how will the cost be affected? 01 3 marks
    • iv) If the transporter from A to R is prepared to reduce the cost by 20% even if one unit 02 transportation business is given to him. Should the offer be accepted?
    • v) If the management wants to embark on an advertisement campaign in one of the market 02 place, which one should be selected? Vi) If the transport cost from C to R decreases from Rs. 11 to Rs.4, what will happen to 02
    • vii) What should be the decrease in the cost of cell A-R so that it used alternatively so 02 that multiple solutions are possible?
    • Q.P. Code :31261 Area Under Standard Normal Distribution

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