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.

- 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**

- 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.
- Neatness and good English will be taken into account.
- Maple should be used in all calculations and plots.
- 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 ``'', ``'', ``'', and ``''
represent constants that you choose at your convenience.

- 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* - MAPLE HELP will be available inTyler 101.
The schedule and location will be announced in
*www.math.uri.edu/Courses/fall02/mth142* - To submit the homework, use the
, for this go to*electronic submission system**www.math.uri.edu*

> 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