The X-Files Makes Me So Angry
Roswell, NM 88201
March 28, 2005
Math 236 Students
Norton, MA 02766
Dear Multivariable Calculus Students:
I have been very upset with the one-sided portrayal of
extraterrestrials in the popular media over the last few years,
so I have decided that
it is time to present a kinder, more capitalist image.
After studying the great hoopla here in Roswell over the years, I have
realized that the best way to destroy Earth is through retail.
I received a grant from the Small Business
Administration for legal aliens, which I plan to use to open several retail
I need help determining where I should locate the central
distribution site, and
when I began looking for consultants,
your enterprising and resourceful professor naturally referred me to you.
My main product will be a scaled-down version of the
Illudium PU-36 Explosive Space Modulator which will be offered
in select, premier outlets across the country.
After careful and meticulous
marketing research, I have decided to open stores in
Mansfield, Massachusetts, Gastonia, North Carolina, Big Spring, Texas, and Kenosha, Wisconsin.
In order to keep inventory costs down, I want to have one central
warehouse for the merchandise, and I will make weekly deliveries
to each of the stores.
I expect to fly three shipments per week to Mansfield, four per week to
Gastonia, two per week to Big Spring, and three per week to Kenosha. Of course, I want to minimize
the shipping costs, so this is where I need your help in determining
where to build the distribution center so that the total flight
distance is as small as possible.
If the market is as strong as I anticipate, I plan to open two more outlets
next summer, one in Thermopolis, Wyoming, and another in Oxnard, California.
I expect the Illudium PU-36 Explosive Space Modulator will be so wildly popular there
that each of these stores will require four weekly trips.
Before I commit to opening these additional outlets, I would
like to know what effect this will have on the location of the
warehouse. I need to know the optimal location for the warehouse if only the
four are open, the optimal location if all six stores are open, and I would
like your recommendation on which location is preferable if I'm uncertain about
which scenario will actually occur.
In order to complete construction and be ready for the summer shopping season,
I would greatly appreciate your report by April 8.
A Few Comments From Your Enterprising and Resourceful Professor
Here are a few suggestions that may help you get started:
- The first thing you will need to do is find appropriate
coordinates for the cities in the xy-plane. You will need to find
the distances between the cities, and then you can pick one of the cities
to be located at the origin. After this, you can find the coordinates for
the other cities.
- There are several web sites that may help you determine the distances
between the cities and locations of airports. A few that
may be useful are the Distance Calculator at
and the AirNav Airport Information at