What is Operations Research (OR)? Explain the 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 2x x 500,2x 5x 1000,4x 6x 1800,x,x 0
[7 marks]Use simplex method to solve following problem: Maximize Z 2x 5x12 Subject to x 4x 24,3x x 21, x x 9,x ,x 0
[7 marks]Use Big-M Method to solve following problem: Minimize Z 12x 20x12 Subject to 3x 4x 50,7x 12x 120,x,x 0
[7 marks]Solve the following using least cost method and North West Corner Method. P Q R Supply A 12 17 14 B 13 13 11 C 15 14 17 D 11 16 2 Demand 7 91 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 20 18 17 22 500 B 22 23 16 20 600 C 18 20 22 24 900 Demand 700 550 450 300
[7 marks]Explain the structure of queuing system in details.
[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]Self-help canteen employs one cashier at its counter, 8 customer arrives every 10 minutes on an average. The cashier can serve at the rate of one customer per minute. Assume Poisson’s distribution for arrival and exponential distribution for service patterns. Determine:
[7 marks]The average number of customers in the system. (ii) The average queue length. (iii) The average time customer spends in the system.
[ 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?2 Year 1 2 3 4 5 6 7 Maintenance cost 100 250 400 600 900 1200 1600 2000
[8 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]Amanufacturer has to supply his customer with 600 units of his product per year. Shortages are not allowed and the storage cost amounts to Rs 0.60 per unit per year. The set up cost per run is Rs 80.00. Find the Optimum run size and the minimum average yearly cost.
[7 marks]