Define Operations Research. List out the applications of OR.
[7 marks]Amarketing manager has five salesman and five sales districts. Considering07 the capabilities of the salesman and the nature of the districts, the marketing manager estimates that the sales per month (in hundred rupees) for each district would be as follows: Districts A B C D E Salesman 2 40 24 28 21 36 Find the assignments of salesman to districts that will result in maximum sales.
[ marks]Obtain the initial basic feasible solution for the following transportation07 problem by using the NWCM and LCM: Retail Shops R R R R R Capacity F 1 9 13 36 51 501 Factory F 2 24 12 16 20 1 100 F 14 35 1 23 26 1503 Requirements 100 70 50 40 40 300
[ marks]Explain reasons for carrying Inventory in detail.07
[ marks]Use the Vogel’s Approximation method (VAM) to find the initial basic07 feasible solution of the following transportation problem: D D D D Supply S 19 30 50 10 71 S S Demand 5 8 7 14 34
[ marks]Explain Calling Population characteristics in context to Queuing System.07
[ marks]Acompany that operates for 50 weeks in a year is concerned about its stocks07 of copper cable. This costs RS 240 a meter and there is a demand for 8000 meters a week. Each replenishment costs Rs 1050 for administration and Rs 1650 for delivery, while holding costs are estimated at 25 % of the value held a year. Assuming no shortages are allowed, What is the optimal inventory policy for the company?
[ marks]Explain types of simulation in detail.07
[ marks]Acompany management and the labour union are negotiating a new three07 year settlement. Each of these has 4 strategies. I: Hard and aggressive bargaining II: Reasoning and logical Approach III: Legalistic Strategy IV: Conciliatory approach The costs to the company are given for every pair of strategy choice. Union Company Strategies Strategies I II III IV I 20 15 12 35 II 25 14 8 III 40 2 10 IV -5 4 11 0 What strategy will the two sides adopt? Also determine the Value of the game.
[5 marks]Write a note on: 1) Events 2) Activities07
[ marks]The data collected in running a machine, the cost of which is Rs. 60,000, are07 given below: Year: 1 2 3 4 Resale Value (Rs): 42,000 30,000 20,400 14,400 9,650 Cost of spares 4,000 4,270 4,880 5,700 6,800 (Rs): Cost of labour 14,000 16,000 18,000 21,000 25,000 (Rs): Determine the optimum period for replacement of the machine.
[5 marks]Amanufacturing company processes 6 different jobs on two machines Aand07 B. Number of units of each job and its processing time on Aand Bare given in the following table. Find the optimum sequence, the total minimum elapsed time and idle time for each machine. Job No. of Units of Processing Time (hours) Number Each Job Machine A Machine B 5 2 9 7.5
[ marks]Given the following table:07 Activity A B C D E F G H I J K L M Predecessor - A B A D E - G J, - A C, I, Activity H K L Duration 6 4 7 2 4 10 2 10 6 13 9 3 (days) Draw a network diagram, indicate the critical path for this project and for each non – critical activity, find the total and free float.
[5 marks]List out the advantages and limitations of Linear Programming.07
[ marks]Obtain the dual problem of the following primal LP problem:07 Minimize Z = x - 3x - 2x x 1 2 Subject to the constraints,
[3 marks]3x - x + 2x ≤ 7 ii) 2x - 4x ≥ 12 iii) - 4x + 3x + 8x = and x , x ≥ 0; x unrestricted in sign.123
[10 marks]Use the simplex method to solve the following LP problem.07 Maximize Z = 3x + 2x + x x 1 2 Subject to the constraints,
[3 marks]2x + 5x + x = 12 ii) 3x + 4x = and x , x ≥ 0; x unrestricted in sign.231
[ marks]Use the graphical method to solve the following LP problem.07 Maximize Z = 2x + x x 1 Subject to the constraints,
[2 marks]x + 2x ≤ 10 ii) x + x ≤ 6 iii) x - x ≤ 2 iv) x - 2x ≤ and x , x ≥ 0.12
[ marks]