What is Operations Research (OR)? What are the significant features of OR? State any four application of OR.
[7 marks]Aperson wants to decide the constituents of a diet which will fulfill his daily requirements of proteins, fats and carbohydrates at the minimum cost. The choice is to be made from four different types of foods. The yields per unit of these foods are given in the following table. Formulate linear programming model for the problem. Food Type Yield per unit Cost per unit Proteins Fats Carbohydrates Minimum Requirements 800 200 700
[7 marks]Solve the following problem using graphical method: Maximize Z 40x 100x12 12x 6x 3000,4x 10x 2000,2x 3x 900,x,x 0
[7 marks]Use simplex method to solve following problem: Maximize Z 2x 5x12 Subject to1 x1 4 x2 2 4 , 3 x1 x2 2 107 , x x 9,x ,x 0
[ marks]Use Big-M Method to solve following problem: Minimize Z 12x 20x12 Subject to 6 x1 8 x2 1 0 0 , 7 x1 1 2 x2 1 2 0 , x1 , x2
[7 marks]Solve the following using least cost method and North West Corner Method. P Q R Supply A 2 7 4 B 3 3 1 C 5 4 7 D 1 6 2 Demand 7 9 18
[14 marks]Solve the following assignment problem. P Q R S T A 11 17 8 16 B 9 7 12 6 C 13 16 15 12 16 D 21 24 17 28 26 E 14 10 12 11 13
[15 marks]Define: Two- person zero- sum game, Saddle point. For the game with payoff matrix: Player B Player A B1 B2 B3 B4 A1 3 −5 0 A2 −4 −2 1 A3 5 4 2 Determine the best strategies for players Aand Band th e value of the game. Is this game (i) fair? (ii) strictly determinable?
[3 marks]Find optimal solution of the following transportation problem. P Q R S Supply A 10 8 7 12 500 B 12 13 6 10 600 C 8 10 12 14 900 Demand 700 550 450 300
[7 marks]Describe the characteristics of calling population (input source) of a queuing system. What do you understand by Queue discipline?
[7 marks]There are 7 jobs, each of which has to go through the machines Aand Bin the order AB. Processing times in hours are given as follow. Determine a sequence of these jobs that will minimize the total elapsed time T. Also find Tand idle time for machines Aand B. Job 1 2 3 4 5 6 Machine A 3 12 15 6 10 11 9 Machine B 8 10 10 6 12 1
[3 marks]What is simulation? Explain Monte-Carlo simulation along with all the necessary steps.
[7 marks]Aself service store employs one cashier as its counter. 9 customers arrive on at average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming passion distribution for arrival rate and exponential distribution for service time, find 1. Average number of customers in the system. 2. Average number of customers in the queue or average queue length. 3. Average time a customer spends in the system. 4. Average time a customer waits before being served.
[7 marks]Explain the difference between PERT and CPM.
[7 marks]The cost of a machine is Rs. 6100 and its scrap value is Rs. 100. The maintenance costs found as follows. When should the machine be replaced? Year 1 2 3 4 5 6 7 82 Maintenance cost 100 250 400 600 900 1200 1600 2000
[7 marks]Aproject has the following characteristics: Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10 Time 4 1 1 1 6 5 4 8 1 2 5 (1) Draw PERT Diagram. (2) Compute Eand Lfor each event. (3) Find the critical path.
[7 marks]Aparticular item has a demand of 9000 units/year. The cost of one procurement is Rs. 100 and the holding cost per unit is Rs. 2.40 per year. The replacement is instantaneous and no shortages are allowed. Determine (1) The economic lot size. (2) The number of orders per year. (3) The time between orders. (4) The total cost per year if the cost of one unit is Rs. 1.
[7 marks]