Chapter 5, Problem 15RE

In problems 15 and 16, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve the problem by the indicated method.

Sail manufacture. South Shore Sail Loft manufactures regular and competition sails. Each regular sail takes $2$ hours to cut and $4$ hours to sew. Each competition sail takes $3$ hours to cut and $10$ hours to sew. There are $150$ hours available in the cutting department and $380$ hours available in the sewing department.

(A) If the Loft makes a profit of $\text{\$}100$ on each regular sail and $\text{\$}200$ on each competition sail, how many sails of each type should the company manufacture to maximize its profit? What is the maximum profit?

(B) An increase in the demand for competition sails causes the profit on a competition sail to rise to $\text{\$}260$. Discuss the effect of this change on the number of sails manufactured and on the maximum profit.

(C) An decrease in the demand for competition sails causes the profit on a competition sail to drop to $\text{\$}140$. Discuss the effect of this change on the number of sails manufactured and on the maximum profit.