## Formulating a Problem for the Simplex Algorithm

The simplex algorithm is used to find optimal combinations of certain quantities, subject to constraints on those quantities. Before the algorithm can be used the problem must be suitably expressed, which involves defining the constraint conditions and the objective function which is to be maximised. Each constrain, and the objective function, is a linear combination of the quantities Suppose a factory produces three types of car A, B and C. The time, money and labour needed to produce each car is shown in the table below.

 Car Time Money Labour A 3 3,000 6 B 5 2,500 9 C 4 2,000 10 Total Available 100 90,000 150

Each car of type A produces £200 profit, each car of type B £350 and each car of type C £150

The total time needed to produce a cars of type A, b cars of type B, c cars of type C is so The total money needed to produce a cars of type A, b cars of type B, c cars of type C is so The total labour needed to produce a cars of type A, b cars of type B, c cars of type C is so Also, of course, and The produced on cars of type A, cars of type B, cars of type C is The simplex algorithm finds values and that maximises the profit subject to time, money and labour constraints.