NATIONAL OPEN UNIVERSITY OF NIGERIA

UNIVERSITY VILLAGE, PLOT 91, CASDASTRAL ZONE, NNAMDI AZIKIWE EXPRESS WAY, JABI, ABUJA.
FACULTY OF SCIENCES
MARCH/APRIL 2014 EXAMINATION

COURSE CODE:                                                                              CIT 425               

COURSE TITLE:                                                                             Operations Research

TIME ALLOWED:                                                                          2 Hours

INSTRUCTIONS:                                                                            Answer any Four (4) Questions

1.(a)    What is Linear Programming. Enumerate at least five assumptions in Linear Programming.    (7 marks)

1.(b)    TRAX Ships a certain refrigerator unit from factories in Lagos and Onitsha to distribution centers in Abuja and Kano. Shipping costs are summarized in the table below:

The supply and demand, in number of units, is shown below:                                      

How should transportation issue be made from Lagos and Onitsha to minimize the transportation cost? (13 marks)

2. (a) Explain the terms: Modelling and Models.                                                               (4 marks)

(b) List and explain five classes of mathematical model.                                              (6 marks)

(c) 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. 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.  (10 marks)

3. (a) Using a tabular form, summarize the various common prototypes, their nature, and model and the techniques for handling each of these prototypes.       (8 marks)

(b) A convalescent hospital wishes to provide at a minimum cost, a diet that has a minimum of 200g of carbohydrates, 100g of protein and 100g of fats per day. These requirements can be met with two foods:                                   

If food A cost 29k per ounce and food B cost 15k per ounce, how many ounces of each food should be purchased for each patient per day in order to meet the minimum requirements at the lowest cost?

Formulate the Linear Programming model.                                                                      (12 marks)

4. (a) State and explain the principle of Optimality                                                           (5 marks)

(b) A company presently operates three manufacturing plants that distribute a product to four warehouses. Currently, the capacity of the plants and demands of the warehouses are stable. These are listed with the unit shipping costs in the following table.

Find the optimal distribution plan for the company                                                         (15 marks)

5. (a) What is Operations Research. Discuss                                                                     (4 Marks)

(b) List and Explain three approaches in the analysis and interpretation of business problem.     (7 marks)

(c) Enumerate briefly explain the various steps involved in the scientific approach to an operation research problem.  (9 marks)

6. (a) Explain Vogel's Approximation Methods, outlining the algorithm involved in this method. (7 marks)

(b) A manufacturing company has divided its total target market into three zones. The Company's marketing department has been collecting data regarding the deployment of salesmen and the sales made in each zones. They have realized that the sales are directly dependent upon the number of sales en in each zone.

The data collected by the company is given in the table below. For various reasons, the company has decided to retain only 9 salesmen during the next year.

Determine the allocation of these salesmen to these three different zones, so that the total sales cabinet is maximized. (13 marks)