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 by the geometric method.

A manufacturing company makes two types of water skis—a trick ski and a slalom ski. The relevant manufacturing data are given in the table below.

(A) If the profit on a trick ski is $40 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit?

(B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $25.

(C) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $45.

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Labor-Hours per Ski Maximum Labor-Hours Department Available per Day Trick Ski Slalom Ski Fabricating 4 108 Finishing 1 24