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Operations Research - May 2016

Mu mechanical engineering (semester 7).

Total marks: -- Total time: -- INSTRUCTIONS (1) Assume appropriate data and state your reasons (2) Marks are given to the right of every question (3) Draw neat diagrams wherever necessary

Attempt any four of the followings

1(b) Explain the terms- i) inventory carrying ii) Optimal order quantity iii) Recorder point. 5 marks

1(c) Explain the terms - Bounded and Unbounded queues. What costs are taken into consideration when decisions made are based queuing theory? 5 marks

1(d) Write dual of following LPP. Maximize, Z = 3x + 5y + 4z Subject to, 3x + 2y + 2z ≤ 2x + 2y + z ≥ 8 x + 2y + 3z = 15 x, y ≥ 0 5 marks

1(e) Solve the following games

2(a) A company manufactures 30 units per day. The sale of these items depends upon demand which has the following distribution:

2(b) At a railway reservation booking window customers arrive randomly at the average rate of 16 per hour approximate to Poisson's distribution. If service time is exponentially distributed with a mean of 20 per hour, determine a) Percentage utilization of capacity b) Probability that there are at least 3 customers in the queue. c) Average time spent in the system d) Average number of customers waiting in the line e) Probability that there are 5 customers in the system. 5 marks

3(a) For organizing four World Cup Cricket matches, cricket clubs of five cities have sent their proposals. The earnings from each match in each city are likely to be different because of the participating teams and local support they enjoy. The expected revenues in lakhs of rupees are as given in following table. How the matches should be assigned to various cities to maximize the expected revenue.

3(b) Solve the following problem using Two Phase method - Minimize: Z = 2x 1 + x 2 Subject to, 3x 1 + x 2 = 3 4x 1 + 3x 2 ≥ 6 x 1 + 2x 2 ≤ 4 x, y ≥ 0 5 marks

4(a) Nagpur Orange Growers Association has three canning factories. Oranges are transported from four orchards. Transportation costs per ton, capacities of orchards and requirements of factories are given in the table. Determine the optimal transportation mix.

4(b) A special purpose machine was purchased for Rs. 10,000. The running cost per year and resale values are given in the following table:

5(a) Hamara Udyog produces large industrial equipment. The firm has received the following orders for its equipments-

5(b) A scooter manufacture requires 40 units of a certain component per day in this assembly line operation. The component is manufactured in the factory itself at the rate of 60 units per day, it costs Rs.150 per unit and set up cost for each production run us Rs.15,000. Inventory carrying cost is Rs.10 per unit per day. If no shortage are allowed, decide the optimal ordering quantity and total estimated system cost. Sketch the inventory system. 5 marks

6(a) A chemical manufacturing company produces two product A and B. Each product passes through three processes. The processing time in hours for each of the two products in each process is given below:

6(b) Explain the terms - Payoff matrix in the context of Game theory and then solve the following games-

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