CIT 425 – OPERATIONS RESEARCH

Instruction:                             Answer Any Five Questions

Time Allowed:                                    3 Hours

1a.        List four basic facts of Operations Research as a concept                                                   4 marks

 b.        Why is Operations Research an adaptation of scientific approach?                         3 marks                   

c.          State the seven stages of Operations Research                                                       7 marks

2.         Solve the following linear programming problem by simplex method.

Maximise Z = 10X1 + 20X2

Subject to the following constraints

3X1 + 2X2 < 1200

2X1 + 6X2 < 1500

X1 < 350

X2 < 200

X1 , X2 > 0                                                                             14 marks

3          A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.

If each scientific calculator sold results in a N2 loss, but each graphing calculator produces a N5 profit, how many of each type should be made daily to maximize net profits?                                          14 marks

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

If food A cost  per ounce and food B cost  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? You are required to formulate the above as a well documented LP model.                                                                                14 marks

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 matter What is the maximum additional advertising expense they can incur in respect of any given product without the manager’s proposal resulting in a smaller profit?                                                                  14 marks

6.         Big Bros. Inc. is an investment company doing an analysis of the pension fund for a certain company. A maximum of million is available to invest in two places. No more than million can be invested in stocks yielding  and at least million can be invested in long-term bonds yielding. The stock-to-bond investment ratio cannot be more than  to. How should Big Bros. advise their client so that the pension fund will receive the maximum yearly return on investment? You are required to formulate the required LP model                                  14 marks.                                                                                                  

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.

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:                      .