Vaughan Ltd makes 2 different types of shoe, Brogue and Casual, each using the same leather and the same skilled labour. The costs of the products per unit of production are as follows:
|
|
Brogue
|
Casual
|
|
|
£
|
£
|
|
Selling price
|
96
|
80
|
|
Materials @ £3 per Kg
|
24
|
12
|
|
Labour @ £12 per hour
|
36
|
36
|
|
Other variable costs
|
12
|
12
|
|
Allocation of fixed costs
|
12
|
12
|
|
|
|
|
|
Profit per unit
|
12
|
8
|
The company is drawing up production plans for the month of June 2012. The anticipated maximum demand in the period is for 50 pairs of Brogues and 80 pairs of Casuals.
There are only 640kg of material and 300 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?
(e) If extra labour became available at £18 per hour should they be employed? If so how many extra hours should be bought?
(f) By how much would the contribution of Casual shoes have to increase by to change your decision in part (c)?