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{\large\bf Name:} \underline{\hskip 3.0 truein}
\hfill
{\large \bf Math 1030 Quiz \#4} (July $24^{\mathrm{th}},$ 2015)

\vspace{0.1in}

\hfill {\large You may {\bf skip ONE} of the following problems.} \hfill \hfill

\vspace{0.1in}

\begin{enumerate}
   \item Emily owns ``Shoes by Twos''. She sells 2000 pairs of a particular style of shoe each year. She can purchase these shoes for \$20 a pair. Shipping costs \$100 per order. Also, it costs her \$1 to store a pair of shoes for a year (base inventory costs on average inventory with all of the standard assumptions). Let $C(x)$ be Emily's annual cost function for these shoes.
   
   \vspace{0.15in}
   
   $C(x)=$ \underline{\hspace{5in}}
   
   \vspace{0.1in}

   List {\bf ALL} of the critical points of $C(x)$ including ``irrelevant'' critical points (points outside the domain of
   reasonable $x$ values). Round each to 3 decimal places.
   
   \vspace{0.15in}

   Critical points: $x=$ \underline{\hspace{5in}}
   
   \vspace{0.15in}

   Emily's {\bf ideal} EOQ is $x=$ \underline{\hspace{1in}} and minimum annual cost is $C(x)=$ \$\underline{\hspace{1.25in}}.
   
\vfill

   \item Let $\displaystyle f(x) = \left\{ \begin{array}{ccc} x^2+2x+7 & & x \leq 1 \\  -x^2-3x+15 & & x > 1 \end{array} \right.$
   \hfill
   Sketch the graph of $y=f(x)$  where $-2 \leq x \leq 3$. 

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   $f(x)$ has \underline{\hspace{1in}} critical points. They are located at $x=$ \underline{\hspace{2in}}.\\
   {}[List {\bf all} critical points. Round to 3 decimal places.]
   
   \vspace{0.1in}
   
   Example of a piecewise function In {\sc Alpha}: The absolute value function can be defined piecewise as
   
   \hfill \verb|piecewise[{{x, x >= 0}, {-x, x < 0}}]| \hfill \hfill
   
\vfill

   \item Bob typically sells 10 sketches when he charges \$50 per sketch. On the other hand, if Bob charges \$20, he typically sells 22 sketches.

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Given this data, Elasticity E = \underline{\hspace{1.5in}}.

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If Bob's point elasticity is ``$\varepsilon = 0.755$'' when he charges \$35 per sketch, should Bob raise or lower his price to increase his revenue? Or has Bob already maximized his revenue?  [Circle the correct answer.]
   
\vspace{0.15in}   
   
{\Large Raise Prices \qquad / \qquad Lower Prices \qquad / \qquad Has Maximized Revenue}
   
   \vfill
   
\end{enumerate}



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