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\line{\bf [COURSE] \hfil \raise -.0in\hbox{\largerbold {\largett Maple}
assignment \#5}\hfil\qquad [DATE]}

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A web page which can help you with this assignment will be linked to
the course webpage. You are encouraged to discuss this assignment with
other students and with the instructors, but the work you hand in
should be your own.

\medskip

A website will be posted listing individualized data for each student.
For this lab, the data will consist of a constraint (restricting a
function's value to 1) and an objective function. Each of these
functions will be polynomials in four variables ($x$, $y$, $z$, and
$w$). You are to find the maximum and minimum value of the objective
function, with candidates restricted to those 4-tuples satisfying the
constraint equation. You should report the max and min values you
find, and the number of points in $\Bbb R^4$ given as candidates using
the Lagrange multiplier method.

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{\parindent=.2in \narrower \noindent 
Please use some care in copying the constraint equation and objective
function. Some of the formulas will be long and elaborate -- this
problem is {\it almost real}.

}

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This assignment is due {\bf [DUE DATE]}. Late
submissions will {\it not}\/ be accepted.

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{\bf Please hand in the following material:} 

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{\parindent=.2in 

\item{0.}All pages should be labeled with your name and section
number. Also, please {\it staple}\/ together all the pages you hand
in.

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\item{1.}A printout of all {\tt Maple} instructions you have
used. (Yes, you may and should ``clean up'' by removing the
instructions that had errors.) 

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\item{2.}Identify clearly in your printout the candidates produced by
using {\tt Maple} to carry out the Lagrange multiplier method using
your data. Be sure to declare explicitly how many different candidates
(4-tuples of numbers) there are.

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\item{3.}Show how {\tt Maple} identifies the maximum and minimum
values, and be sure to identify these numbers clearly.

}
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