# National Open University Exam Past Question – CIT 425 MAY/JUNE 2012 EXAMINATION

## NATIONAL OPEN UNIVERSITY OF NIGERIA CIT 425 OPERATIONS RESEARCH

14-16 AHMADU BELLO WAY, VICTORIA ISLAND LAGOS SCHOOL OF SCIENCE AND TECHNOLOGY

MAY/JUNE 2012 EXAMINATION

CIT 425 OPERATIONS RESEARCH Time Allowed:  3 Hours

 1a. Define Operations Research 3 marks b. List and explain the stages in Operations Research 14 marks c. State the role of Operations Research in business 3 marks 2a. Differentiate between the following mathematical models: Quantitative and Qualitative Probabilistic and Deterministic Linear and Non Linear                                                                   1 2 marks
1. State an approach for transforming a word problem into a mathematical program      8 marks

3           ONIJOGBO manufactures two types of settee; half-upholstered and full-upholstered. The contribution per unit to profit is  N80 for half-upholstered and  N90 for full-upholstered. The amount of materials needed per product and maximum available materials are given below:

 Product Unit of Material Wood Foam Cover Half-upholstered 2 2 5 Full-upholstered 1 4 5 Maximum available 12 24 35

You are required to                                                                                                           formulate the linear programming model for the above problem

20  marks.

1. Solve the linear program

Max     x1         + x2

Subject to:                2X1 +X2    ≤ 4

X1    +2X2 ≤  3

With:                        X1 ≥ 0, X≥ ≥ 0

5           The sales manager of Turnover Limited maintains he could increase the sales turnover (in units) of any of the company’s product by 50 percent if he was authorized to give a 10% price discount and place appropriate additional advertising matter

Required:

The Board wishes to know the maximum additional advertising expense they can incur in

respect of any given product without the manager’s proposal resulting in a smaller profit

20 marks.

1. Big Bros. Inc. is an investment company doing an analysis of the pension fund for a certain company. A maximum of #10 million is available to invest in two places. No more than

#8 million can be invested in stocks yielding 12%

and at least

#2 million can be invested in

long-term bonds yielding 8% . The stock-to-bond investment ratio cannot be more than 1 to 3 . How should Big Bros. advise their client so that the pension fund will receive the maximum yearly return on investment?

Formulate the required LP model                                                                           20 marks.

1. 7. A farmer has 100 acres on which to plant two crops: corn or wheat. To produce these crops, there are certain expenses as shown in the table.

 Item Cost per Acre (# ) Corn Seed Fertilizer Planting/care/harvesting 12 58 50 Total 120 Wheat Seed Fertilizer Planting/care/harvesting 40 80 90 Total 210

After the harvest, the farmer must store the crops awaiting proper market conditions. Each acre yields an average of 110 bushels of corn or 30 bushels of wheat. The limitations of resources are as follows:

Available capital:

#15,000

Available storage facilities:

4,000

bushels.

If net profit (the profit after all expenses have been subtracted) per bushel of corn is #1.30 and for wheat is #2.00 , how should the farmer plant the

100 acres to maximize the profits?

20 marks

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