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Important announcement: (Last date of submission for January 2023 session is 30th April, 2023 and for July 2023 sessions is 31st October, 2023)
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?
July 2022
1. What is operations research? What are the characteristics of operations research? Discuss the significance and scope of operations research in modern management.
2. A construction company has undertaken three projects, one each in City A, City B and City C. Each project requires a specific supply of raw material which the firm sources from the Cities D, E, F, and G. Shipping costs (in rupees) differ from location to location. The following table summarizes the problem the manager of the construction firm faces:
The contractor learns that due to some difficulties, currently no shipments are possible between the cities D and A, and between F and C.
a) Obtain the optimal transportation plan for the contractor. Calculate the total cost. At what location is some supply going to be short? By how much?
b) Is the solution in (a) is unique. If not, identify another optimal solution.
c) Write the dual of this problem and use the values of the dual variables to check the optimal solution.
3. What is Goal programming? What are the steps involved in Goal programming model formulation? Discuss the applications of Goal programming with suitable examples.
4. A manufacturing company uses Rs. 10,000 worth of an item during the year. He has estimated the ordering costs as Rs. 25 per order and carrying costs as 12.5$ of average inventory value. Find the optimal order size, number of orders per year, time period per order and the total cost.
5. Write a short note on the following:
i. Characteristics of a queuing model
ii. Zero – sum two person games.
iii. Steps in the simulation process.
iv. Random experiment and probability.
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IGNOU MS51 MBA Assignment Question
1. Five candidates are approved for appointment as personal secretaries to five members of the board of a company. The preferences of each member are given below. How would you make allocations so that satisfaction level is maximized?
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2. In an engineering workshop, motor breakdown at an average of 5 per day, the number of breakdown being Poisson distributed. The present unqualified mechanic can repair motors at an average rate of 6 per day and is paid Rs. 100 per day. A qualified mechanic offers his services at Rs. 200 per day and is capable of repairing at an average of 8 motors per day. When a motor is idle, there is downtime cost incurrence at the rate of Rs. 100 per day. Would it be worthwhile to employ the qualified mechanic in place of the present mechanic? Justify on cost/ benefit analysis.
3. Determine which course of action Player B will not use in the following game. Obtain the best strategies for both players and the value of the game.
4. “Operations Research is a logical and systematic approach to provide a rational basis for decision making.” Explain the phases and processes of Operations Research Study.
5. Write the short note on the following:-
(a) Binomial Distribution
(b) Cutting plane method for solving Integer Programming
(c) Limitations of Simulation
(d) Objectives of Inventory
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