A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour to make, whereas each pair of trousers takes 40 minutes. The materials for a jacket cost $32 and those for a pair of trousers cost $40. The company can devote only 34 hours per week to the production of jackets and trousers, and the firm’s total weekly cost for materials must not exceed $1200. The company sells the jackets at a profit of $12 each and the trousers at a profit of $14 per pair. Market research indicates that the firm can sell all of the jackets that are produced, but that it can sell at most half as many pairs of trousers as jackets.

a- How many jackets and trousers should the firm produce each week to maximize profit?

b- Due to the changes in demand, the company has to change its profit margin on a pair of trousers. Assuming that the profit margin on a jacket remains at $12 and the manufacturing constraints are unchanged, find the minimum and maximum profit margins on a pair of trousers which the company can allow before it should change its strategy for optimum output.