Question One

Biochemicals Perspective, an organic chemical company in the UK,produces two main products, FATAS and APOL. The market prices and the resource requirements for producing 1 kg of each of the two products are:

SellingCost ofProcess 1 Process 2PriceMaterialsLabourLabour

Hours Hours

FATAS135.0017 4 4

APOL122.5015 2 5

Labour in process 1 costs 10 per hour.Labour in process 2 costs 15.50 per hour. Currently there is a maximum of 3,500 hours per year available in Process 1 and 4,550 hours per year available in Process 2.

FATAS is a long established product where demand has been reducing over the years.The sales director expects demand on this product to be limited to 500 kg this year. He also insists that 150 kg of APOL have to be produced to satisfy an influential customer.

Required

1. Formulate the linear programme for the optimum production plan for the spare capacity available.

(5 marks)

2. Solve the linear programme formulated above either by the graphical method or simplex method.

(8 marks)

A solution to the linear programme is given in the final tableau below:

S_1, S₂ and S₃ are slack variables for Process 1, Process 2 and maximum demand for FATAS respectively.

FAS₁S₂S₃Solution

S₁00 1-0.4-2.4480

A01 00.2-0.8360

F10001500

Z0 0028 11,600

3.Interpret the information given in the final tableau.

(8 marks)

4.Investigate the effect on the solutions of each of the following:

( i) an increase of 10 hours per year in Process 2;

(ii) an increase of 15 kg per year in the output of FATAS assuming that the extra output can be sold.

(4 marks)

(Total: 25 marks)