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\Huge{
First Applications}
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Get into groups of two or three people and work on the front of this worksheet.  \emph{Do not} start on the back side yet. 

\begin{enumerate}
\item The market price for widgets is \$.50.

\begin{enumerate}
\item Draw the revenue function for a company selling widgets.

\includegraphics[height=2in]{Blank200By150}


\item Find the revenue function ($R$) for a company selling $q$ widgets.
\vskip .5in
\item Estimate the marginal revenue at the 101$^{\text{st}}$ widget.
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\item Use (b) to find $R'(100)$ algebraically.
\vskip 2in
\item Copy the cost function presented in class onto the graph on the front page.  What number of widgets will give the company a profit?
\vfill
\item What amount of widgets sold will maximize the company's profit?

\end{enumerate}




\newpage
\emph{Do not} start on this until the lecture on 2.5 is over.  The following problems are meant to give you some practice over the material from \S 2.5 and all of chapter two since the exam is next Tuesday.  
\item An industrial production process costs $C(q)$ million dollars to produce $q$ million units; these units then sell for $R(q)$ million dollars.  If $C(2.1)=5.1$, $R(2.1)=6.9$, $MC(2.1)=0.6$, and $MR(2.1)=0.7$, find the following:
\begin{enumerate}
\item The profit earned by producing 2.1 million units.
\vskip .5in
\item Should the company increase or decrease production to maximize profit?
\vskip 1in
\item The approximate change in revenue if production increases from 2.1 to 2.14 million units.  
\vskip 1in
\item The approximate change in profit if production increases from 2.1 to 2.14 million units.  
\vskip 1in
\end{enumerate}

\item Some good practice problems to help prep you for the exam:
\begin{enumerate}
\item Review on page 130: \#1,2,7-12, 19, 21,26
\item If $f(x)=3x^2-x$, find $f(-2)$ algebraically.
\item If $g(x)=\frac{1}{x}$, find $g(x)$ algebraically.
\end{enumerate}

\end{enumerate}

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