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Sensitivity Analysis 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 Labour Labour

Hours Hours

C 75 4 5

B 60 5 2.5

Labour in Process 1 costs 9 per hour. Labour 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

1. Formulate the linear programme for the optimum production plan using the existing resources available. (4 marks)

A solution to the linear programme 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 S₁ S₂ S₃ Solution

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

2. 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)

3. 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)

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