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        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

 

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)