Bramble Ltd makes 2 different types of boots, Premier and Champion, each using the same leather and the same skilled labour. The costs of the products per unit of production are as follows:
|
|
Premier
|
Champion
|
|
|
£
|
£
|
|
Selling price
|
80
|
60
|
|
Materials @ £8 per Kg
|
4
|
3
|
|
Labour @ £15 per hour
|
15
|
10
|
|
Other variable costs
|
12
|
8
|
|
Allocation of fixed costs
|
30
|
20
|
|
|
|
|
|
Profit per unit
|
19
|
19
|
The company is drawing up production plans for the 3 months to 30 June 2011. The anticipated maximum demand in the period is for 800 pairs of each type of boot.
There are only 630kg of material and 1500 hours of labour available in the period.
The company wishes to maximise profit in the period
Required
(a) Formulate a linear programming model for this problem.
(b) Prepare the initial tableau if the problem is to be solved using simplex
(c) Use the graphical method to determine how many of each type of boot should be produced
(d) What are the shadow prices of materials and labour? What do these prices mean?
(e) If new supplies of leather became available at £12 per kg should they be purchased? If so how much extra material should be bought?
(f) By how much would the contribution of champion boots have to increase by to change your decision in part (c)?