\documentclass[12pt,fleqn]{article}
\pagestyle{empty}
\setlength{\topmargin}{-1in}
\setlength{\oddsidemargin}{-.3in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{7.2in}


\begin{document}

\begin{center}
{\Large TEST 4

Math 1090 - 2}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
Use the back of the pages if necessary.
\vspace{.1in}

Name \rule{5in}{.2pt}

\vspace{.2in}

\begin{enumerate}

\item  \label{vw1}
You spend some time researching VW camper vans and 
studying their acceleration.
You test the following model:
The time $t$, in \emph{minutes}, that it takes a Volkswagen camper van
to accelerate to $x$ miles per hour can be modeled by the equation:
\[
t = .01(-597.62+.1976x^2 +21.017x)
\]
How fast can the camper van go after 11 minutes?
(Your answer may not reflect the acceleration in your car, 
but remember that this is a VW.)

\item  The percentage of (U.S.) workers that belong to unions from 
1930 to 1989 can be modeled by the following equation
where $t$ in in years past 1900, 
and $u$ is the percentage of workers belonging to unions in that year.
\[
u = -39.3213 + 2.38432t - .022129 t^2
\] 
Did the percentage of workers belonging to unions reach a maximum or a minimum?
When did this occur, and what was the maximum or minimum percentage?

\item  Graph the function.
Find the coordinates of the vertex and label it.
Find the zeros and label them too.
\[
y=-2(x^2+x)-8x-13
\]

\item  You and a friend are making bumper stickers.
You make 2 varieties: simple ones, and fancy ones.
The simple sticker takes 15 minutes to make and the fancy ones take 30 minutes
to make.
You sell the simple stickers for \$2 each and the fancy ones for \$3 each.
Between the two of you, you have 30 hours total per week to make stickers.
The sticker market is such that you can only sell a total of 75 stickers
each week.
How many of each stickers should you make of each type 
to maximize your revenue?
(Hint: I would convert to hours first.
To get full credit you have to find the right inequalities,
and graph the inequalities.)

\end{enumerate}

\end{document}







