Although decision problems with limiting factors usually involve the maximisation of contribution, there may be a requirement to minimise costs. A graphical solution, involving two variables, is very similar to that for a maximisation problem, with the exception that instead of finding a contribution line touching the feasible area as far away from the origin as possible, we look for a total cost line touching the feasible area as close to the origin as possible.
A minimisation problem
Claire Speke has undertaken a contract to supply a customer with at least 260 units in total of two products, X and Y, during the next month. At least 50% of the total output must be units of X. The products are each made by two grades of labour, as follows.
|
Grade A labour
|
X Hours
4
|
Y Hours
6
|
|
Grade B labour
|
4
|
2
|
|
Total
|
8
|
8
|
Although additional labour can be made available at short notice, the company wishes to make use of 1,200 hours of Grade A labour and 800 hours of Grade B labour which has already been assigned to working on the contract next month. The total variable cost per unit is $120 for X and $100 for Y.
Claire Speke wishes to minimise expenditure on the contract next month. How much of X and Y should be supplied in order to meet the terms of the contract?