Thread: Linear Programming Help

This is my first example of linear programming with ratios and I'm not really sure what to do. I need help finding the constraints and then I can work the rest out myself.

Here's the question:
The owner of a factory that manufactures kitchen units has a contract to supply at least 72 units per week.
*He employs x artisans and y apprentices
*He cannot accommodate more than 16 employees.
*The Apprentices Act states that the ratio of apprentice to artisans is not greater than 9:2
*The Trade Union Act rules require that the ratio of apprentices to artisans is not smaller than 1:2.
*An artisan can produce 9 units per week while an apprentice can produce 6 units per week.

1. Write down a system of inequalities to represent the information above.

I can do the rest of the questions myself, just need to know the constraints.

The solution should be similar to what you see below, provided I did not make any mistakes.


Let x be the number of artisans and y the number of apprentices.

0 <= x + y <= 16 (he cannot accommodate more than 16 employees - note that you cannot have -1 employees, hence the greater than or equal to zero )

1/2<y/x<9/2 (ratios of apprentices to artisans).

Now, for the number of units,

0<= 9x + 6y <= 72 (an artisan produces 9 units while an apprentice produces 6)