Exercise 1 Usage of free production capacity A factory has ended a non-profitable production line. As a result, there is a reasonable amount
of free production capacity available. The management team considers to use this capacity for
manufacturing one or more of the products A, B and C. Before a product can be sold it has to be
treated by 3 machines. The table below shows the available capacity per machine and the amount
of hours required to manufacture a product:
Machine type Available capacity Product A Product B Product C
(hours per week)
Machine 1
500
9
3
5
Machine 2
350
5
4
0
Machine 3
150
3
0
2
It is expected that each unit of product A and B that is manufactured can be sold, while the
number of sales of product C is at most 20 units per week. The profit per unit is 50, 20 and 25 Euro
for product A, B and C, respectively. The manufacturing team wants to maximize total profit.
Formulate this problem as a linear programming problem and explain which decision variables are
used.