Bachelor of Management Studies (B.M.S.) SEM VI 2017 18 Nov 2017-18 OPERATION RES 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/ illustrations, wherever necessary
4. Q6 Graph paper will be supplied on request
5. Q1 any two from the following:
   • a) for a sick person must contain at least 18 units of vitamins, 12 units of minerals and 10 units of 7.5 calories. Two foods F, and F2are available at a cost of Rs. 4 and Rs. 8 per unit respectively. One unit of Ficontains 6 units of vitamins, 1 unit of minerals and 3 units of calories. One unit of food 1 units of vitamins, 4 units of minerals unit of calories. Formulate the problem as LPP and solve it graphically to minimize the total cost
   • b) Solve by using Simplex method. 7.5 Subject to constraints
   • c) Answer the following:
   • i) Explain “infeasibility” in LPP using graphical sketch. 2.5
   • ii) Explain limitations of Operations Research. 2.5
   • iii) What isa unique optimal solution? How do you test is unique in Simplex method? 2.5
6. Q2 Attempt any two from the following:
   • a) acompany is transporting its units from three factories Fi, F2 and F3 to four warehouse Wi, W2, W3and Wa. The supply and demand of units with transportation cost per unit (in Rs.) are given below
   • ii) Test IFS for optimality using MODI method and find optimal solution. 04
   • Q.P. Code :01855
   • b) A departmental head has four subordinates who differ in efficiency and the tasks differ in their 7.5 intrinsic difficulty. His estimate of the time each man would take to perform each given in the How should the tasks be allocated on one to one basis to minimize the total man-hours? Find optimal assignment of men and tasks Time (in hours)
   • c) Answer the following:
   • i) What is Degeneracy in transportation problem? How to resolve it? 2.5
   • ii) Explain regret matrix in assignment problem. 2.5
   • iii) How do you detect and find multiple optimal solutions to an assignment problem? 2.5
7. Q3 Attempt any two from the following:
   • a) Asmall project consists of following six activities
   • i. Draw network diagram. Find critical path and project completion time. 03
   • ii. Find EST, EFT, LFT, LST and Total float for all activities. 4.5
   • b) .A project consists of the activities A,B,C,D,E,F and G whose time estimates and given below:
   • i. Find expected time and variance of all activities. 03
   • iii. Find probability of project completion in 15 days. 15
   • Q.P. Code :01855
   • c) Answer the following:
   • i. What is critical path in PERT CPM analysis? 2.5
   • ii. Define optimistic, pessimistic and most likely times in PERT. 2.5
   • iii. What is project crashing? 2.5 Attempt any two from the following :
   • a) Acompany has a choice of adopting any one out of four courses of action A1, A2, A3, A4. There are four possible states of nature S1, S2, $3, S4. Find optimal decision using each of the following decision
   • ii. Maximax 01
   • iii. Laplace 1.5
   • iv. Hurwicz (x= 0.4) 02
   • B) Consider the following pay off matrix
   • i. Find the Maximin Strategy. 2.5
   • ii. Find the Minimax Strategy. 2.5
   • iii. What is the value of the Game? 2.5
   • C) In afactory there are 6 jobs which are to be performed on two machines A and B in the order AB. The processing time (in minutes) for the jobs are given below
   • i. Determine the optimum sequence for performing jobs. 02
   • iii. Idle time for each machine. 02
   • Q.P. Code :01855 From four warehouse A, B, C and D the stocks are to be transported to four market are W, Z. The supplies from warehouses are 100, 100, 150, 250 tons respectively. Whereas the requirement of markets are 180, 160, 160, 100 tons respectively. The cost matrix (in Rs. per unit) and to the problem is given in the following table
   • i. Is the above solution feasible? justify 1.5
   • ii. Is the above solution non-degenerate? Justify. 1.5
   • iii. Is the solution optimal? Find by using MODI method and also find optimal transportation cost. 04
   • iv. Is there more than one optimal solution? Justify. 02 Calculate the opportunity cost to the route ‘A to Y’ and ‘C to Y’. 02 Vi. What should be the minimum unit cost of the cell B to X so that the company can optimally use this route alternately? 02 Vii. If the transport carrier offers discount of 75 % on existing cost for the route A to Z should the management accept the offer. Justify. 02
   • Q.P. Code :01855 Area Under Standard Normal Distribution

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