% (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\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 }


\centerline{\bf Math 106---Calculus II\quad Project 2}
\centerline{\bf \dots still living in an industrial world}
\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
As highly successful independent mathematical and scientific technical
contractors, celebrating the successful completion of your largest
contract to date, you have just received a new contract---clearly a
direct result of your past success.  The letter you received from
Chemproc, Inc. (recently purchased by the MPC, Inc.\ conglomerate)
on the subject of their recently initiated chemical processing factory
follows.
\vfill\eject

\logo
\medskip
\longindent 20000 Ryan-ears Blvd.\par
\longindent Lonlinc, SK\par
\longindent 04685\par
\medskip
\longindent 8 October, 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
As you know, Chemproc, Inc.\ has recently opened a chemical
reprocessing plant in East Lonlinc.  After an immensely successful
start, we are just beginning the planning for the establishment of the
third of the four chemical reprocessing lines at this plant.  This
line is concerned with the purification of water having chemical
toxins dissolved in it, a byproduct of the chemical processes involved
in several industrial applications.  To avoid the cost of disposing of
this waste-water, the companies contract with us to remove the toxins.
\medskip
\noindent
The purification of the water is accomplished by forcing it through
the system shown in figure 1.  As it passes through the system, it is
exposed to the chemically active surface of the conduit, which reacts
with the dissolved toxins in the water to produce a solid precipitate.
This precipitate is filtered out by the filters shown in the figure.
\bigskip
\hbox{\indent\indent\psfig{figure=cal2_prj2fig.eps,width=5.5in}}
\bigskip
\noindent
Because the efficacy of this process is dependent on the (chemically
active) surface area of the conduit, we need an accurate assessment of
this area.  This is the first information we are contracting with
you to determine.
\medskip
\noindent
Additionally, we are concerned with the energy requirements to force
the water through the system.  The second item in your contract is
therefore to determine the work that will be required of the pump we
will use to drive the system.
\medskip
\noindent
As specified in your contract, your report should be submitted by the
27$^{\rm th}$ of this month, when our board of directors next meets.
If you should find in the course of your investigation that you have
questions regarding this project, you are to contact Dr.\ Gavin
LaRose, our consulting scientist (whose services we obtained following
our recent merger with M.P.C.\ Inc.) with
the other members of your investigative team; he will be more than
willing to assist you.  You should further contact him (also as a
team) by the 18$^{\rm th}$ to report on your progress.

\medskip
\noindent 
We look forward to seeing your finished report, which should conform
to the enclosed technical report requirements.
\bigskip

\longindent Yours sincerely,
\bigskip
\bigskip
\bigskip
\longindent E. Idu Pont, President\par
\longindent Chemproc, Inc.
\bigskip
\bigskip
\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 Chemproc,
Inc. be written so that all members of the board of directors can
understand and apply the information contained therein.  These board
members are all experts in their respective areas of chemical
processing, 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
