May 2017 Q4

a) A particular linear programming problem is formulated as follows:
Minimize z = 2500x + 3500y
Subject to constraint:

Required:
i) Draw these constraints on the same graph paper.                                                                                                           (6 marks)

ii) Determine the optimum solution.                                                                                                                                  (6 marks)

b) Managers within a subsidiary company in a conglomerate want to know how to maximize the profit from two types of products X and Y. Each product X requires one hour of labour and six litres of molding material, whereas each product Y requires two hours of labour and five litres of molding material. The total labour hours available for each week is 40 and the total amount of molding material each week is 150. The profit contribution from product X is GH¢20 and from product Y is GH¢ 30.
Required:
Formulate, the linear programming model for the problem.                                                                                              (8 marks)