1. A company manufactures two products, X and Y, using machines A, B, and C. Machine A has 4 hours of capacity available during the coming week. Similarly, the available capacity of machines B and C during the coming week is 24 hours and 35 hours, respectively. One unit of product X requires one hour of Machine A, 3 hours of machine B and 10 hours of Machine C. Similarly, one unit of product Y requires 1 hour, 8 hours and 7 hours of machine A, B and C, respectively. When one unit of X is sold in the market, it yields a profit of Rs. 5/- per product, and that of Y is Rs. 7/- per unit. Formulate a linear programming model and solve this problem using the graphical method to find the optimal product mix.
2. ‘Linear programming is one of the most frequently and successfully employed Operations Research techniques to managerial and business decisions’. Elucidate this statement with some examples.
3. Explain, by taking an illustration, the North-West Corner rule, the Least Cost Method and the Vogel’s Approximation Method to obtain the initial feasible solution to a transportation problem.
4. What is a stage in dynamic programming? Explain the steps involved in solutions to dynamic programming problems.
5. Discuss the assumptions underlying the basic EOQ formula. Also, state the economic order quantity model, discuss its sensitivity, and explain its significant extensions.
1. The ABC Company has been a producer of picture tubes for television sets and certain printed circuits for radios. The company has just expanded into full-scale production and marketing of AM and AM-FM radios. It has built a new plant that can operate 48 hours per week. Production of an AM radio in the new plant will require 2 hours, and production of an AM-FM radio will require 3 hours. Each AM radio will contribute Rs 40 to profits, while an AM-FM radio will contribute Rs 80 to profits.
The marketing department, after extensive research has determined that a maximum of 15AM radios and 10 AM-FM radios can be sold each week
a) Formulate a linear programming model to determine the optimum production mix of AM and FM radios that will maximize profits.
b) Solve this problem using the graphical method.
2. Discuss briefly:
a) The general similarities between dynamic programming and linear programming.
b) How dynamic programming differs conceptually from linear programming?
3. A company has three plants at locations A, B, and C, which supply to a warehouse located at D, E, F, G, and H. monthly plant capacities are 800, 500 and 900 units, respectively. Monthly warehouse requirements are 400, 400, 500, 400 and 800 units. Unit transportation costs (in `) are given below. Determine an optimum distribution for the company in order to minimize the total transportation cost.
4. What constitutes inventory ordering costs, carrying costs and stock-out costs? Explain the behaviour and relationship of these costs.
5. A has two ammunition stores, one of which is twice as valuable as the other. B is an attacker who can destroy an undefended store, but he can only attack one of them. A can successfully defend only one of them. A learns that B is about to attack one of the stores but does not know which. What should he do?
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