Pre-Calculus Student
Franklin & Marshall College
Lancaster, PA 17604
Dear Pre-Calculus Student:
I am working on a grant proposal and I need help from someone who knows
mathematics. I got your name from my friend Susan Laglander at the Bungle
Brewery.
Let me begin by introducing the organization I represent. The North American
Horned Duck Society (N.A.H.D.S.) is dedicated to the preservation of the North
American horned duck, which is close to extinction. In spite of its name, the
duck doesn't really have horns, just prominent head feathers.
The greatest threat to the survival of the North American horned duck comes
from the interstate highway system. The ducks like it, that is, they always
make their migratory flights above interstate highways. Perhaps you've seen the
ducks as you've been driving. No one knows exactly why they do this, but our
researchers have theorized that they are attracted to "parallel lines" and have
a weak sense of direction. This is a disastrous combination at large
intersections, which seem to confuse the ducks. Half of the time they head east
or west and end up in places like New York City or St. Louis, which are no
places for horned ducks.
The N.A.H.D.S. is working hard to save the duck. We support breeding programs
designed to increase the number of ducks in the near future. We are
investigating the feasibility of training older ducks (the leaders) to "fly
straight". We are advocating for long term solutions such as camouflaging
east-west interstate highways to make them less appealing to the ducks.
As you may imagine, we need funding to continue such important work, and that
is why we are working with Laglander and the Bungle Brewery on our latest
project. We are applying for a grant from the federal Small Business
Environmental Protection Administration for Bungle to build a solar brewery. As
part of the deal Bungle will donate to us a percentage of the profits from
selling their new Ecobrew.
I am finishing our grant application and I want to include a distinctive design
for the Ecobrew can. Since we are emphasizing ecology, I think we should use as
little aluminum as possible to make each can. It has to hold 12 oz. of the brew
(Laglander says that is the same as 22 cubic inches) and it has to be shaped
like other cans (they are all cylinders, according to Laglander). What we don't
know is how tall and how wide should we make the can in order to use the least
aluminum? It seems to me that it shouldn't be too tall or we will have to use
too much aluminum to make the side. On the other hand, it shouldn't be too
short because then it will have to be wider (in order to hold 12 ounces of the
brew) and we will use too much aluminum to make the top and bottom. The answer
must be somewhere in the middleI'm sure someone who knows as much math as you
could figure it out.
If you can reply by Friday, December 2, I can include the design of the
"eco-can" in our proposal, which is due the next day at the Small Business
Environmental Protection Administration. Thank you for taking time out of your
busy schedule to help us with this problem.
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