Question $5$: $(6$ marks$)$

A small business enterprise makes dresses and trousers. To make a dress requires $4$ hours of cutting and $2$ hours of sewing. To make a trouser requires $2$ hours of cutting and $4$ hours of sewing. The profit on a dress is $12$ Dhs and on a trouser $22$ Dhs The business has a maximum of $64$ hours of cutting time and $96$ hours of sewing time to operate per week.

a$.$ Determine how many dresses and trousers should be made to maximize profit. $(4$ marks$).$

b$.$ What is the maximum profit? $(2$ marks$)$

Maximize the following profit function:

Subject to the constraints: