Math Problem Solver

Product Mix Problem

The manager in a manufacturing firm is considering devoting the excess capacity to one or

more of products: 𝑃1, 𝑃2, 𝑃3, 𝑃4, 𝑃5 and 𝑃6.

The machine time (in minutes) required per unit are:

Machine Type 𝑷𝟏 𝑷𝟐 𝑷𝟑 𝑷𝟒 𝑷𝟓 𝑷𝟔

Milling machine 17 14 13 18 7 10

Lathe 15 0 14 7 12 0

Grinder 13 11 13 14 11 13

The available machine time (in hours) per week is 128+a, 200+b, 130+c for Milling, Lathe

and Grinder machines respectively. The sale people estimate they can sell all the units of

𝑃1, 𝑃2 and 𝑃3 that can be made at respective prices of £10, £7 and £9. The first 20 units of

𝑃4, 𝑃5 and 𝑃6 produced per week can be sold at £10 each, but all made in excess of 20 can

only be sold at £6 each. Variable labour costs are £4 per hour for Milling and Lathe machines,

while Grinder machine labour costs £3 per hour. Material costs are £3 for each product of

𝑃1, 𝑃3 and 𝑃5, while each product of 𝑃2, 𝑃4 and 𝑃6 only cost £2. The manager wishes to

maximise the firm's weekly profit