Business-modeling-average-cost.tex

\Section{Business modeling---average cost}
\label{sec:biz-mod-avg-cost}

\begin{ProblemSet}[pencil space=1in]
 \begin{Problem}
  Conceptually, the \emph{average cost function} takes as its input a number that means what?
 \end{Problem}
 \begin{Problem}
  Conceptually, the \emph{average cost function} produces as its output a number that means what?
 \end{Problem}
 \begin{Problem}
  If $C(x)$ is the cost function for a business, what is the general equation for the average cost function?
 \end{Problem}
 \begin{Problem}
  Suppose it costs $10 + 3x + 0.1 x^2$ dollars to produce a unit of a product.
  Sketch the average cost function, using an $x$-range of $0$ to $50$ and a $y$-range of $0$ to $20$.
  \bigskip

  \GraphingGridSmall
 \end{Problem}
\end{ProblemSet}

\newpage
Consider the following scenario.
Cougar Caf\'e sells muffins.
Based on past sales figures, the manager estimates that to sell $x$ packs of muffins per day, the price of a pack of muffins should be
\begin{equation*}
 20.0 - 0.12 x \text{ dollars }
\end{equation*}
The cost to make $x$ packs of muffins is
\begin{equation*}
 3 + 4.25 x + 0.09 x^2 \text{ dollars }
\end{equation*}


\begin{ProblemSet}[pencil space=1in]
 \begin{Problem}
  What is the cost function?
 \end{Problem}
 \begin{Problem}
  What is the marginal cost function?
 \end{Problem}
 \begin{Problem}[pencil space=2in]
  What is the average cost function?
 \end{Problem}
 \begin{Problem}[pencil space=2in]
  What is the marginal average cost function?
 \end{Problem}
\end{ProblemSet}

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