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© 2014 Pacific Crest
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A
Successful Performance
Successful application of your learning looks like this
As you begin to apply what you’ve learned, you should have a good idea of what success looks like.
A SUCCESSFUL
PERFORMANCE
I produce solutions to quantitative problems using the Problem Solving Methodology. I...
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Use mathematics to build effective and accurate sub-model solutions
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Integrate sub-solutions seamlessly to produce an overall solution
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Validate the sub-solutions and overall solution with the problem definition as the
target
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Document every step of PSM so others can review my work
D
emonstrate Your Understanding
Apply it and show you know in context!
1. Final Course Evaluations: Your instructor’s department chair realizes that the student evaluations
used do not address the unique features of this class and has asked your class to design a new form.
The purposes of the student course evaluations are: to assess your instructor’s performance, to assess
the appropriateness of the curriculum, and to assess the general class atmosphere. Additional items
may be included; however, you are limited to one standard size page.
2. Cylindrical Tank: Determine the least expensive way of building a cylindrical tank which will hold
10,000 cubic feet of gasoline. Assume that metal costs $5 per square foot and welding costs $2 per
linear foot. Metal is available in sheets up to 8 feer wide by 20 feet long.
3. Tower of Cans: One of the long-standing sight gags in movies and on televisions is that of a shopper
extracting a single can from a pyramidal tower of cans, only to watch the entire pile come tumbling
down. Exactly how many cans are in such a tower?
Assume that the tower has a triangular base, and that each can rests on a triangular support of cans
below it (with the obvious exception of the bottom layer). If the top layer consists of a single can,
find the total number of cans in a pyramid 20 layers high.
5. Pet Cost for One Year: How much does it cost to support a pet for a year?
6. Recycling Economics: What economic system would you put in place to guarantee a 75% recycling
of aluminum, glass, and paper.
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Model, the Methodology, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the hardest problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems. Try to determine which of the steps are the hardest
and what types of situations make these steps the hardest.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make problem solving difficult?
4.2 Applying the Problem Solving Methodology