A chemicals company produces two main products, C and B. The market price of C is 205

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Question:

A chemicals company produces two main products, C and B.

The market price of C is £205 and that of B is £155 per 100 kg. The resource requirements for producing 100 kg of each of the two products are:

Cost of Process 1 Process 2

Materials Labor Labor

£ Hours Hours

C 75 4 5

B 60 5 2.5

Labor in Process 1 costs £9 per hour. Labor in Process 2 costs £12 per hour. During the coming period the company will have the following resources available:

Process 1 3,000 hours

Process 2 2,500 hours

C is a long established product where demand has been reducing over the years. The company expects the demand on this product to be limited to 15,000 kg this year.

Required

A solution to the linear programmed is given below:

S₁,S₂ and S₃ are slack variables for Process 1 and Process 2 and the maximum demand for Product C, respectively.

Final Tableau

C B S₁S₂S₃Solution

B 0 1 0.2 0 -0.8 480

S₂ 0 0 -0.5 1 -3 550

C 1 0 0 0 1 150

Z 0 0 4 0 18 14,700

1) Interpret the information given in the tableau above and show that it would be worthwhile paying the labour in Process 1 for overtime working at £11.00 per hour

(6 marks)

2)Calculate how many extra hours in Process 1 could be worked on overtime before another binding constraint is created and calculate the extra contribution this would make.

(2 marks)