DFG manufactures two products from different combinations of the same resources. Unit selling prices and unit cost details for each product are as follows:

Product

X

Y

per unit

per unit

Selling price

120

115

Direct material A at 5 per kg

10

20

Direct material B at 3 per kg

24

12

Skilled labour at 7 per hour

21

28

Variable overhead at 2 per machine hour

18

14

Fixed overhead*

36

28

Profit

11

13

*Fixed overhead is absorbed using an absorption rate per machine hour. It is an unavoidable central overhead cost that is not affected by the mix or volume of products produced.

The maximum weekly demand for products X and Y is 450 units and 400 units respectively and this is the normal weekly production volume achieved by DFG. However, for the next four weeks the achievable production level will be reduced due to a shortage of available resources. The resources that are expected to be available are as follows:

Direct material A

1,800 kg

Direct material B

3,500 kg

Skilled labour

2,500 hours

Machine hours

6,500 hours

(a) Calculate the contribution of each product.2 marks

(b) Determine the optimal production plan for X and Y to maximise the contribution earned. You should use linear programming, identify the constraints, identify the feasible region by drawing a graph and determine the contribution of each relevant point within the feasible region using simultaneous equations where necessary.18 marks