Math 141 - Calculus I - Spring 2009 – Prof.
Janeba
Project #1
GOALS:
- To gain experience dealing with realistic "open-ended" problems
for
which there may not be a simple numerical answer. The answer may
take
many forms and needs to be explained in detail through the use of
words,
numbers, formulas, and graphs.
- To gain experience explaining mathematical results in English.
- To practice working with others on a mathematical problem.
- To become familiar with the members of the group with whom you
will be working on these projects.
Your group is a consulting firm. The Mega Corporation has invited
you
to submit an entry in the competition it will use to select a
consulting
firm for the next five years. Mega wants the competitors to use
the
following assumptions:
- Mega Corp, headquartered in Freedonia, must use luxury
rental
cars fairly often. Since Freedonia is small it has only two car
rental
companies, Hurts and Fudget. Each company offers only one luxury
car rental deal:
- Hurts: $120 per day and 30¢ per mile,
but there is an allowance of 100 free miles per day.
- Fudget: $90 per day plus 40¢ per mile. No allowance
of free miles.
- The daily charge is for a 24 hour period beginning when the car
is picked
up. Any part of a day is charged at the full rate. (Thus a
25 hour rental
from Hurts would cost $240 plus mileage charge.)
- Both companies pay for all of the fuel used. (Freedonia
hasn’t had an energy crisis yet).
- Either company has enough cars to supply all of the required
rentals.
- Mega has no preference between the companies or the cars that
they offer.
Consequently, Mega will accept a policy which uses either company
exclusively
or a mixture of both.
- The maximum length of time for which a car is rented is two weeks.
- The maximum distance ever driven during a rental period is
1500 miles.
Your problem as a consulting firm is to submit a set of guidelines for
car
rental in Freedonia which will minimize Mega's car rental
expense. In making
its selection of a consulting firm, Mega will be examining:
- The correctness and completeness of your mathematics,
- Your clear and complete explanation of the logic behind your
recommended guidelines, and
- The correctness and completeness of your exposition. Also,
- The clarity of the guidelines and the ease of their use,
especially for not-so-clear-thinking Mega employees.
- This means you will want to present your findings on two
levels: One one level, an easy-to-use guideline for Mega
employees which doesn't require much thought to use. One another
level, in keeping with #2 and #3 above, a clear (and probably separate)
explanation for Mega executives as to why that guideline is best
according to the criteria above.
- Your firm's ability to handle similar, though possibly more
complicated,
problems in the future – as evidenced by the level of sophistication
your firm demonstrated with this
problem.
Consulting firms will be required to make a private group presentation
to
Mega's designated competition coordinator, Prof. Janeba, on either
Thursday, January 22, or Friday, January 23. Please make an
appointment with
Prof. Janeba - there are limited appointments available on each day.
Come
to your appointment with a significant portion of your guidelines
already
worked out, preferably in written form.
Final reports are to be on 8.5x11 inch white paper sheets bound with
a single staple, submitted to the Mega Corporation office (Collins 202)
no
later than 4 pm, Thursday, January 29, 2009. Anything
simply
shoved under the door after the secretary leaves at 4 pm that day will
be
assumed to have been too late!
A Word to the wise: This project is worth about 10% of your course
grade.
Please take it seriously. In the past, some students who did not
take
it seriously enough had unpleasant surprises. Please carefully
read
all the instructions and resources provided.
Last Modified January 18, 2009..
Prof.
Janeba's Home Page | Send comments or questions to:mjaneba
willamette.edu
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