In Problem 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.

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 $100 on each regular sail and $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 $260. Discuss the effect of this change on the number of sails manufactured and on the maximum profit.

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