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\noindent
{\bf Math 1030 Workshop \#6} \hfill
{\bf Name: \underline{\hspace*{2.5in}}}

\vspace{0.05in}

\noindent
{\Large \bf DUE: Monday, August 1${}^{\mbox{st}}$} \hfill Please turn in a paper copy and {\bf SHOW YOUR WORK!}

\vspace{0.05in}

\begin{enumerate}
   \item  Slimy Stan sells bootleg Koalas smuggled in from Australia (don't ask how it's done). Stan has collected the following Koala demand and price data:

\hfill
\begin{tabular}{|c||c|c|c|c|} \hline
Koalas Sold \varspace{0.25in}{0.01in} & 10   & 75  & 150 &  300 \\ \hline
             Price \varspace{0.25in}{0.01in} & \$3,000 & \$1,500 & \$1,000 & \$425 \\ \hline
\end{tabular}  
\hfill \hfill

\begin{enumerate}[(a)]
   \item Compute elasticity (round to 3 decimals places):

\begin{tabular}{|c||c|c|c|c|} \hline
\hspace*{0.05in} Koalas Sold \varspace{0.25in}{0.01in} & 10   & 75  & 150 &  300 \\ \hline
            Price \varspace{0.25in}{0.01in} & \qquad \$3,000 \qquad{} & \qquad{} \$1,500 \qquad{} & \qquad \$1,000 \qquad{} & \qquad \$425 \qquad{} \\ \hline
\end{tabular}  

\vspace{-0.025in}
    
\begin{tabular}{|c|c|c|c|c|} \hline
 \mbox{\parbox[c][0.4in]{1.46in}{Elasticity}} & \varspace{0.2in}{1.025in} & \varspace{0.2in}{1.025in} & \varspace{0.25in}{0.925in} & \mbox{\parbox[c][0.2in]{0.335in}{ $\times\mbox{ }\times$\\$\times\mbox{ }\times$ }} \\ \hline
\end{tabular}

\vspace{0.1in}

   \item Model this demand price (in Excel) using an {\bf logarithmic} trendline. 

\vspace{0.15in}

            $p_d(q) =$ \underline{\hspace{2in}}

\vspace{0.15in}

           According to this model, Stan will sell \underline{\hspace{1.5in}} Koalas if he sets his price at \$700. 

\vspace{0.15in}

           When $p_d(q) = \$700$, our point elasticity (using this model) is $\varepsilon =$ \underline{\hspace{1.25in}} (round to 3 decimal places).

\vspace{0.15in}

          \underline{Circle the correct answer:} \qquad Stan is currently charging \$700 for a Koala and wants to {\bf increase} his revenue, he should \varspace{0.5in}{0.01in}
         \quad {\Large raise \quad / \quad lower} \quad his price.
        
\vspace{0.05in}

What quantity and price will {\bf maximize} revenue? \quad $q =$ \underline{\hspace{1in}}  \quad $p=$ \underline{\hspace{1in}}

        
\end{enumerate}

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   \item Suppose that some item's point elasticity is $\varepsilon = 0.7$ at some price. If the quantity is lowered by 7\%, \dots
   
   \vspace{0.25in}
   
   the price is {\Large \quad lowered \quad / \quad raised \quad} by \underline{\hspace*{2in}} 
      
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   and revenue is {\Large \quad lowered \quad / \quad raised \quad} by \underline{\hspace*{2in}}. 
   
   [Both answers should be percentages rounded to 3 decimal places.]

\vspace{0.5in}

\vspace{0.1in}
              
   \item George is renting some cheap space downtown. His storage room is quite oddly shaped and he wants to figure out its square footage. Starting at the the edge of his room George measures how wide the room is using a tape measure. He steps 2 feet over each time he makes a measurement. This is what he found\dots 

\force \hfill   
   \begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|c|} \hline
   Feet from edge: & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\ \hline
         Room width: & 15 & 17 & 18 & 16 & 16 & 17 & 19 & 17 & 17 & 16 & 15 \\ \hline
   \end{tabular}
\hfill \force 

\vspace{0.1in}

Approximate the room's square footage in 2 different ways: (1) Using a right hand rule approximation with $n=10$ rectangles and (2) Using Simpson's rule with $n=10$. [Round each answer to 3 decimal places.]

\vspace{0.15in}

Right hand rule: \underline{\hspace{1in}}  \hfill
Simpson's rule: \underline{\hspace{1in}}  \hfill

\vspace{0.15in}

\newpage

   \item Suppose that $R(t)=1000t^2e^{-t/5}$ models the rate of production of kitchen grease powered cars where $t$ is the number of years since January 1, 2000. 
   
   \vspace{0.25in}
   
   When (after the peak production) will the production rate drop to 10 grease cars per year? $t=$ \underline{\hspace{1.5in}}\\ 
   \force \hfill  [Round to 3 decimal places.]
   
   \vspace{0.25in}
   
   The maximum production rate will be \underline{\hspace{1in}} grease cars per year. This will occur when $t=$ \underline{\hspace{1in}}.
   
   \vspace{0.25in}
   
   How many grease cars will be produced after January 1, 2017? \underline{\hspace{2in}}.\\
      
   \vspace{0.25in}
   
   When will the 100,000${}^{\mathrm{th}}$ grease car be completed? \underline{\hspace{2in}}. \\
   \force \hspace{3.5in} [Give the month and year.]
      
   \vspace{0.1in}
   
   {\sc Alpha} Commands used / integrals computed:
   
   \vfill
   
   \item Stacy has a rather impressive collection of shoes (not all of which even fit her feet). She has about 3,000 pairs of shoes. Assuming that her collection of shoes has a normal distribution of sizes (with a mean size of 8.5 and a standard deviation of 1.25), answer the following questions:

{\it Note:} Women's shoe sizes go up by $1/2 = 0.5$.  Although there is a difference of opinion about this, consider 4 to be the smallest size. This means that the interval: $-\infty < t \leq 4.25$ represents the smallest size $4$ and then $4.25<t<4.75$ represents size $4.5$ etc.
   
   \vspace{0.25in}

    How may pairs of shoe sizes 8 to 11 does she have? \underline{\hspace{2.5in}}
  
   \vspace{0.25in}
  
   How many shoes size 6 and under does she own? \underline{\hspace{1.75in}}
  
   \vspace{0.25in}
  
   How large does a pair of shoes need to be to make it into the largest 3.5\% of her collection? \underline{\hspace{1.75in}}
       
   \vspace{0.1in}
   
   {\sc Alpha} Commands used / integrals computed:
   
   \vfill
  
\end{enumerate}

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