Modeling Project 1 MTH 142 Spring 2000

The Stained Glass Co. (SGC) is a well known company that sells many products. SGC has been doing very well since it became fashionable in urban America to have a house with at least one window with stained glass. Orders have been pouring in, particularly from large corporations specialized in construction. The following is a design that initially sold very well, but whose recent sales are dissapointing:

The Market Research Unit of SGC has determined that buyers want new designs. As a member of the Industrial Design Unit of the Stained Glass Co. you have been given the assignment of producing two designs for a window acording to the specifications listed below.


SPECIFICATIONS

[ S1]
The shape is a square.
[ S2]
Each design should have exactly two colors, ``dark" and ``light"
[ S3]
The curves that determine the design are given in terms of formulas.
[ S4]
No color should account for more than 80 % of the total area.
[ S5]
Each design should have at least six regions.
[ S6]
Each design should have regions determined by 3 different curves.
Also, you are supposed to issue a REPORT with the following sections.
Section 1: Name of Project, author, class/section, date.
Section 2: A complete, informative and clear description of the project in your own words.
Section 3: Proposed design number 1. Supply
3.a )
A plot of the design. (Use the auxiliary function found in the worksheet ftp://www.math.uri.edu/pub/merino/StainedGlassCo.mws )
3.b )
The formulas for boundary functions.
3.c )
A calculation of the areas corresponding to light and dark colors. (Explain carefully all the steps. Use Maple.)
3.d )
The percent of the total area for each color.
Section 4: Proposed design number 2. Include subsections as in Section 3.
Section 5: Conclusions. Compare the different designs, and state the weak and strong points of each. State whether you believe if the designs meet the specifications.

COMMENTS and additional information

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The final project should have only one author. You may discuss the project with your classmates, but what you turn in should contain your own original designs.
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Neatness and good English will be taken into account.
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Maple should be used in all calculations and plots.
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You may use many curves in your designs. Here is a list of models that you may use (in addition to the ones you may come up with). In the formulas below, the letters ``$a$'', ``$b$'', ``$r$'', and ``$c$'' represent constants that you choose at your convenience.

\begin{displaymath}
\begin{array}{ll}
\mbox{\rm Lines: } & y = m x + b, \quad x ...
...thmic: } & y = a \, \ln \vert \, x - b \, \vert + c
\end{array}\end{displaymath}

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For basic information on Plotting, solving equations and calculating integrals in Maple: see the Maple worksheet `` Introduction to Maple in Calculus II''(intro142.mws) , located in www.math.uri.edu/Center/workc2.html
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MAPLE HELP will be available inTyler 101. The schedule and location will be announced in www.math.uri.edu/Courses/fall02/mth142
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To submit the homework, use the electronic submission system, for this go to www.math.uri.edu
USEFUL MAPLE COMMANDS


> restart;                 # good to have this at the top of worksheet; 
> with(student);           # adds extra functionality
> with(plots);             # adds extra functionality for plots (recommended)
> f:=x->x^2;               # define a function f(x)
> g:=x->evalf(x^3);        # define a function f(x), force it to give decimal result
> plot(f(x),x=-1..1,y=0..2,scaling=constrained); #uses same scaling in x and y axes. 
> plot(f(x),x=-1..1,y=0..2,axes=boxed); #a plot in boxed form. 
                           # Note: the option tickmarks=[0.0] eliminates ticks.
> plot([f(x),g(x)],x=0..2);# plot two functions for x between 0 and 2.
> solve(f(x)=g(x),x);      # solve the equation f(x) = g(x) for x.
> int(f(x),x=1..2);        # integrate f(x) for x between 1 and 2.
> Pi ;                     # the number 3.1415...Note the it begins with capital P.
> exp(2.5);                # exponential function evaluated at 2.5
> ln(2.5);                 # the natural logarithm of 2.5

© 2002 O. Merino