National Open University Exam Past Question – CIT 425 OCTOBER/NOVEMBER 2014 EXAMINATION

NATIONAL OPEN UNIVERSITY OF NIGERIA CIT 425   – OPERATIONS RESEARCH

14-16 AHMADU BELLO WAY, VICTORIA ISLAND LAGOS SCHOOL OF SCIENCE AND TECHNOLOGY OCTOBER/NOVEMBER 2014 EXAMINATION

CIT 425   – OPERATIONS RESEARCH

INSTRUCTION:  Answer any four questions                                                        Time: 2 HOURS

1. 1. (a) Define what is Operation Research.                                                                              (2 Marks)

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

(c)    Enumerate and briefly explain the various steps involved in the scientific approach to an operation research problem.                                                                          (11 Marks)

 2. (a) Define these terms; Modeling and Models. (4 Marks) (b)   (c) Explain at least four types of Models used in OR.   Outline and explain five classes of mathematical model. (6 Marks)   (10 Marks)

1. (a) Using a tabular form, summarize the various common prototypes, their nature, 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 120g

of fats per day. These requirements can

be met with two foods:

 Food Carbohydrates Protein Fats A   B 10g   5 g 2 g   5 g 3g   4 g

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)

1. (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 the 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)

 PLANTS WAREHOUSES MONTHLY CAPACITY A                       B                       C                       D X 3 16 9 2 40 Y 1 9 3 8 20 Z 4 5 2 5 50 Monthly Demands 25 25 42 8 110       100

1. (a) Explain the term Linear programming and outline at least five assumptions in its procedure.                                                                                           (7 Marks)

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

 Source Destination Shipping Cost Lagos Abuja   Kano N30   N40 Onitsha Abuja   Kano N60   N50

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

 Supply Demand Lagos,                 200 Abuja,               300

Onitsha,             600        Kano,                400

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

1. (a) Explain Vogel’s Approximation Method, outlining the algorithm involved in this method.(7)

(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 salesmen 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 cab net is maximized.                                                                                        (13 Marks)

 No. of Salesmen Profits in Thousands of Naira Zone 1 Zone 2 Zone 3 35 40 45 1 40 50 50 2 45 65 60 3 60 75 70 4 70 85 80 5 80 95 90 6 90 100 100 7 105 105 110 8 100 100 120 9 90 105 100

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