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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.

\begin{tabular}{|l|c|c|}
\hline
Department & Trick Ski & Slalom Ski \\
\hline
Fabricating & 9 & 6 \\
\hline
Finishing & 1 & 1 \\
\hline
\end{tabular}

Answer parts (A), (B), and (C) below:

(A) If the profit on a trick ski is [tex]$\$[/tex] 40[tex]$ and the profit on a slalom ski is $[/tex]\[tex]$ 50$[/tex], how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit?

The maximum profit is [tex]$\$[/tex] 1350$. The maximum occurs when 0 trick skis and 27 slalom skis are produced.

(B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to [tex]$\$[/tex] 35$.

The maximum profit decreases to [tex]$\square$[/tex] [tex]$\$[/tex] \square[tex]$. The maximum occurs when $[/tex]\square[tex]$ trick skis and $[/tex]\square$ slalom skis are produced.

(C) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to [tex]$\$[/tex] 60$.

The maximum profit [tex]$\square$[/tex] increases to [tex]$\$[/tex][tex]$ $[/tex]\square[tex]$. The maximum occurs when $[/tex]\square[tex]$ trick skis and $[/tex]\square$ slalom skis are produced.



Answer :

GinnyAnswer
(A)

If the profit on a trick ski is [tex]$40 and the profit on a slalom ski is $[/tex]50, to realize the maximum profit, 0 trick skis and 27 slalom skis should be manufactured each day.

The maximum profit is therefore \( \$1350 \).

(B)

If the profit on a slalom ski decreases to [tex]$35, the maximum profit decreases to \( \$[/tex]945 \). The optimal production schedule remains the same, with 0 trick skis and 27 slalom skis being produced.

(C)

If the profit on a slalom ski increases to [tex]$60, the maximum profit increases to \( \$[/tex]1620 \). The optimal production schedule remains the same, with 0 trick skis and 27 slalom skis being produced.

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