For the 2015 – till date past questions for this course CLICK HERE
Contact me for your TMA, GST302 Business plan writeup, Project Writeup and also get your Exam Summary for this course.
NATIONAL OPEN UNIVERSITY OF NIGERIA
14/16 AHMADU BELLO WAY, VICTORIA ISLAND, LAGOS
SCHOOL OF SCIENCE AND TECHNOLOGY
MARCH/APRIL 2014 EXAMINATION
COURSE CODE: CIT 756
COURSE TITLE: OPERATIONS RESEARCH
TIME ALLOWED: 3 HOURS
INSTRUCTION: Answer any five questions.
1 Using the Simplex method, Solve the linear programming.
Max x1 + x2
Subject to: 2X1 +X2 ≤ 4
X1 +2X2 ≤ 3
With: X1 ≥ 0, X≥ ≥ 0
2a. What do you understand by modeling and models? 5 marks
b. 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. 9 marks
3a. Discuss the Vogel’s Approximation Method, clearly enumerating the algorithm involved in this method. 5marks
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 Onitsha, 600 | Abuja, 300 Kano, 400 |
How should transportation issue be made from Lagos and Onitsha to minimize the transportation cost? (9 Marks)
4. 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. 14 Marks
| No. of Salesmen | Profits in Thousands of Naira | ||
| Zone 1 | Zone 2 | Zone 3 | |
| 0 | 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 |
5 The sales manager of Turnover Limited maintains he could increase the sales turnover (in units) of any of the company’s product by percent if he was authorized to give a price discount and place appropriate additional advertising matterThe 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 profit14 marks
6. (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 (9 Marks)
| PLANTS | WAREHOUSES A B C D | MONTHLY CAPACITY | |||
| 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 |
7. A farmer has 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 | |
| Total | |
| Wheat | |
| Seed | |
| Fertilizer | |
| Planting/care/harvesting | |
| Total |
After the harvest, the farmer must store the crops awaiting proper market conditions. Each acre yields an average of bushels of corn or bushels of wheat. The limitations of resources are as follows:
Available capital: .
Available storage facilities: bushels.
If net profit (the profit after all expenses have been subtracted) per bushel of corn is and for wheat is , how should the farmer plant the acres to maximize the profits? 14 marks
For the 2015 – till date past questions for this course CLICK HERE
Contact me for your TMA, GST302 Business plan writeup, Project Writeup and also get your Exam Summary for this course.
