Question

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)

Answer 1

a. Formulate the linear programme for the optimum production plan using
the resources available
Ans.
Let the company produce x kg of Product C and y kg of product B
	Market price	Cost of materials $	Process 1 labour hrs	Labour cost per hour $	Process 1 labour cost	Process 2 labour hrs	Labour cost per hour $	Process 2 labour cost	Profit per 100 kg
C	205	75	4	9	36	5	12	60	34
B	155	60	5	9	45	2.5	12	30	20
The linear programming problem for the question can be formulated as follows
Suppose we want to maximize the profit of producing product C and product B
	Maximize Z = 34x + 20y
	Subject to
	4x + 5y <= 3000	Process 1 labour hours
	5x + 2.5y <= 2500	Process 2 labour hours
	x <= 15000	Product C demand limitation