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Q- A manufacturer of outdoor clothing makes wax jackets and trousers. Each jacket requires 1 hour...

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Advance Math

Q- A manufacturer of outdoor clothing makes waxjackets and trousers. Each jacket requires 1 hour to make, whereaseach pair of trousers takes 40 minutes. The materials for a jacketcost $32 and those for a pair of trousers cost $40. The company candevote only 34 hours per week to the production of jackets andtrousers, and the firm’s total weekly cost for materials must notexceed $1200. The company sells the jackets at a profit of $12 eachand the trousers at a profit of $14 per pair. Market researchindicates that the firm can sell all of the jackets that areproduced, but that it can sell at most half as many pairs oftrousers as jackets.

  1. A- How many jackets and trousers should the firm produce eachweek to maximize profit?

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

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