% (c) 1996 Gavin LaRose (glarose@NebrWesleyan.edu)
% permission is granted to use and distribute for free
% in an academic setting
% 
\nopagenumbers
\input psfig.sty
%\font\headerfont=cmdunh10 at 18 truept
\font\headerfont=ccsl10 at 14.4 truept
\font\sevenrm=cmr7
\def\longindent{\hskip 4in}
%\def\logo{\hrule
%     \medskip
%     \hbox to \hsize{\vrule height 0pt width 3.9in depth .4pt
%     \lower 1.5ex \vbox{\headerfont Chemproc, Inc.} }
%     \medskip
%     \hrule }
\def\logo{\longindent{\headerfont M.P.C., Inc.}
          \smallskip
          \hrule
          \medskip }

\centerline{\bf Math 106---Calculus II\quad Project 3}
\centerline{\bf \dots }
\centerline{\sevenrm \copyright 1995 Gavin LaRose
(glarose@NebrWesleyan.edu), Nebraska Wesleyan University}
\centerline{\sevenrm permission granted to use and distribute for 
free in an academic setting.}

\bigskip
Success is yours, and the contracts are pouring in!  After two
resoundingly successful contracts with large companies (both,
curiously, related to the giant MPC, Inc.\ conglomerate), you have
received a third such contract.  The letter you received from the MPC,
Inc.\ conglomerate comes on the heels of their use of your previous
correspondence with regards to the expansion of their world-wide
headquarters, and follows.
\vfill\eject

\logo
\medskip
\longindent 1 MPC Drive\par
\longindent Lonlinc, SK\par
\longindent 04685\par
\medskip
\longindent 20 November, 1995\par

\bigskip
\bigskip

\noindent Sophisticated Technical Contractors, Inc.\par
\noindent Suite 1, Strawmarket Business Plaza\par
\noindent Lonlinc, SK 04685

\bigskip
\bigskip

\noindent Dear STC:
\medskip
\noindent
We were favorably impressed by your cost analysis for the different
expansion proposals which we were considering earlier this Fall, and
so have contracted with you for additional analysis as we move in the
construction phase of the expansion.

\medskip
\noindent 
Because of recent legislation passed by the Lonlinc city board, we
are having to lay a new line from the local power hub to provide
electronic connectivity and power.  Unfortunately, this necessitates
running conduit through the wetlands behind the new
construction, and calculating the cost of laying it therefore becomes
complicated by the fact that the expense is proportional to the amount
of water saturating the soil.  We therefore need from you an accurate
estimate of the amount of water in the soil that we will have to dig
through to lay the conduit.

\medskip
\noindent
To determine the amount of water along the path that the conduit will
be laid our in-house engineers took measurements at intervals along
the path; their results are summarized in Table 1, below.
\bigskip
\hbox to \hsize{
\hsize=1.75in
\vbox{\item{} {\bf Table 1.} \% water saturation in
ground along conduit path.}
\hsize=4.75in
\indent
\raise -.2in
\vbox{
\hrule
\halign{\vrule # & \strut#\hfil & 
         \hfil # \hfil & \vrule #\quad & 
         \hfil # \hfil & \vrule #\quad & 
         \hfil # \hfil & \vrule #\quad & 
         \hfil # \hfil & \vrule #\quad & 
         \hfil # \hfil & \vrule #\quad & 
         \hfil # \hfil & \vrule #\cr

        & $x = $ (yds) &      0    && 1      && 9      && 12   
                && 18     && 21     &\cr
        & \% H$_2$O =  &    10.0\% && 10.5\% && 16.0\% && 17.5\%
                && 23.5\% && 24.0\% &\cr
\noalign{\hrule}
        & $x = $ (yds) &      33     && 34     && 45     && 47
                && 58     && 60     &\cr
        & \% H$_2$O =  &      25.0\% && 26.5\% && 42.0\% && 40.0\%
                && 19.5\% && 17.0\% &\cr
}
\hrule
}
\hfil
}

\bigskip
\noindent
The ditch to be dug for the conduit is shown schematically in Figure
1.
\bigskip
\hbox to\hsize{
\hsize=2in
\vbox{\item{} {\bf Figure 1.} Ditch and conduit configuration.}
\hsize=4.25in
\indent\indent
\raise -.25in
\vbox{\psfig{figure=cal2_prj3fig.eps,width=2in}}
\hfil}

\bigskip
\noindent
In as much as we hope to have a full budget outline for the expansion
project finished by the end of the calendar year, we need your
estimate for the the cost of the ditch (you are to assume that the
cost of the ditch, per cubic foot of water in the soil, is \$$C$%$
) by
the 15$^{th}$ of December at the very latest.  If you have questions
as you are working on the project, you should consult with chief
scientist, Dr. Gavin LaRose, who has been instructed to assist you
insofar as may be possible.  Please also note that you should be in
touch with him at the ends of the weeks of the 27$^{th}$ of November
and 4$^{th}$ of December to update us on your progress.  As is usual,
we have enclosed a copy of our technical report specifications, which
should govern the presentation of your results.
\bigskip

\longindent Yours sincerely,
\bigskip
\bigskip
\bigskip
\longindent Warren Fubbet, President\par
\longindent MPC, Inc.
\bigskip
\noindent Encl: Technical report requirements

\vfill
\eject

\logo
\bigskip
\centerline{\bf Technical Report Requirements}
\bigskip
\noindent
It is of paramount importance that the reports submitted to MPC,
Inc.\ be written so that all members of the board of directors can
understand and apply the information contained therein.  These board
members continue to be well educated, but for their mathematical
background should be assumed only to remember one semester of
calculus.
\bigskip
\noindent Reports should further:
\bigskip
\item{$\bullet$} Be written in the first person plural.
\medskip
\item{$\bullet$} Include mathematical formulas in the report as
appropriate to describe the methods used and results obtained.
\medskip
\item{$\bullet$} Clearly explain how the mathematical formulas that
are included bear on the problem being solved, and how the solution(s) 
obtained answer(s) the question(s) that the report is to answer.
\medskip
\item{$\bullet$} Consist of 
\smallskip
\itemitem{$\bullet$} An {\sl Introduction\/}, indicating generally the
problem(s) to be solved, and giving an explanation of the organization
of the remainder of the report.
\smallskip
\itemitem{$\bullet$} A section for each of the problems considered,
each having
\smallskip
{\narrower
\itemitem{$\bullet$} An {\sl Introduction\/}, specifically
describing the 
problem to be solved, and an indication of the mathematical method used to
solve it.
\smallskip
\itemitem{\qquad $\bullet$} A {\sl Body\/}, describing the mathematical
problem that was solved to answer the question(s) posed in the
introduction, and the solution to it.
\smallskip
\itemitem{\qquad $\bullet$} A {\sl Conclusion\/}, summarizing the
results 
obtained from the solution described in the body and clearly stating
their relevance to the original problem as described in the
introduction. 
\medskip
}
\item{$\bullet$} Be 2$1\over 2$--5 pages in length.

\bye
