Example: Product planning

(This type of problem is also called Product Mix Problem)


A manufacturing firm produces two products, A and B. Each of these products must be processed through two different machines. One machine has 24 hours of available capacity, and the second machine has 16 hours. Each unit of product A requires three hours of time on both machines. Each unit of product B requires two hours of time on the first machine and one hour on the second machine. The profit is $8 per unit of product A and $6 per unit of product B, and the firm can sell as many units of each product as it can produce. The objective of the firm is to maximise profits. The problem is to determine how many units of product A and product B should be produced within the limits of available machine capacities.

2. Tables:

The numerical information from text are better organised in table (tables):
  Time requirement on first machine (hours) Time requirement on second machine (hours) Profit ($ per unit)
Product A 3 3 8
Product B 2 1 6
Total time available on fist machine (hours) 24
Total time available on second machine (hours) 16