Roswell, NM 88201
March 28, 2005

Math 236 Students
Wheaton College
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 outlets. However, 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 www.indo.com/distance and the AirNav Airport Information at http://www.airnav.com/airport.