Business-modeling-optimization.tex

\Section{Business modeling---optimization}

A retailer sells specialized tires.
It costs
\begin{equation*}
 200 + 25 x + 1.5 x^2 \text{ dollars}
\end{equation*}
to produce and sell $x$ tires per month,
where $1 \leq x \leq 25$.

They can sell $x$ tires per month if the price is
\begin{equation*}
 600 - 18 x \text{ dollars.}
\end{equation*}

\begin{ProblemSet}

 \begin{Problem}[pencil space=4in]
  How many tires should they sell per month to maximize profit?
  Give your answer to the nearest tenth, as in $12.3$.
 \end{Problem}

 \begin{Problem}[pencil space=1in]
  At what price should a tire be sold to maximize profit?
  Give your answer to the nearest cent.
 \end{Problem}

 \begin{Problem}[pencil space=1in]
  What is the maximum profit?
  Give your answer to the nearest cent.
 \end{Problem}

 \begin{Problem}[pencil space=5in]
  How many tires should they sell each month to minimize average cost?
 \end{Problem}

 \begin{Problem}[pencil space=1in]
  What is the minimum average cost?
  Give your answer to the nearest cent.
 \end{Problem}

 \begin{Problem}[pencil space=1in]
  What is the profit when the average cost is minimized?
 \end{Problem}

\end{ProblemSet}

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