Chapter 5.3, Problem 49E

In Problems 49-64, 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.

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

$\begin{array}{l}\begin{array}{ccc}& \text{ Labor-Hours per Ski }& \end{array}\\ \begin{array}{cccc}\text{Department}& \text{Trick Ski}& \text{Slalom Ski}& \begin{array}{l}\text{Maximum Labor-Hours}\\ \text{Available per Day}\end{array}\\ \text{Fabricating}& 6& 4& 108\\ \text{Finishing}& 1& 1& 24\end{array}\end{array}$

(A) If the profit on a trick ski is $\text{\$}40$ and the profit on a slalom ski is $\text{\$}30$, 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 $\text{\$}25$.

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