# Math 105--Calculus I: Project 3, Fall 1997

## An Illuminating Project...

### by Gavin LaRose (glarose@umich.edu), Nebraska Wesleyan University, October 1997

permission granted to use and distribute free in an academic setting.

DVI file of project---needs the EPS figure, which should be named "p3f1.eps"
PostScript version of project

## The letter from Welbilt...

### Welbilt Design and Construction, Inc.

6533 Haybaler Highway
Lonlinc, SK 0485

12 November 1997

Independent Mathematical Contractors, Inc.
Lonlinc, SK 04685

Dear IMC:

Having been satisfied with your work on a number of other contracts with which we have charged you in the past, we are at Welbilt Design and Construction again commissioning your services in support of a recent job that we have obtained with the Lonlinc Airport Commission. In an effort to improve the quality of the air transportation offered to its citizens, the LAC has recently embarked on an effort to renovate and expand the well-used airport in Lonlinc.

As a major contractor for parts of this reconstruction, Welbilt is in charge of the new lighting to be installed in the airport. The modern, attractive fixtures to be installed are shown in figure 1.

Figure 1: Light Fixture

As can be seen in the figure, the light emanates from the fixture in a direct manner through an arc of angle phim measured up from the vertical. The specifications of the bulbs to be installed in the fixtures indicate that the intensity of the light shed by the bulb varies as the sine of the angle from the vertical, phi, reaching zero at either end of the light-emitting aperture. The intensity of the light hitting the floor is obviously also dependent on the distance from the bulb to the point on the floor being considered, varying inversely as the square of the distance from the fixture to that point (e.g., the point P in figure 1). The intensity of the light reaching P is therefore the product of these two effects.

To properly plan the positioning of these fixtures, we need to know where on the floor under the fixtures the intensity of the direct light is the greatest, and it is to obtain an estimate for this that we are contacting you. As we need to have a full report for the LAC by mid-December, we need your final report on this matter by the 8th of December. To facilitate your work, we have arranged with a local mathematical expert and friend of ours, the redoubtable Dr. let-us-not-forget-the-P. Gavin LaRose, to serve as a contact for any questions you may have in your work. You should contact him with a report of your progress by the 19th of November and again by the 3rd of December. Any failure to meet these deadlines will result in an arbitrarily large penalty to your grade.

We look forward to hearing from you.

Sincerely
Frankyl O. Y. Drite
President, Welbilt Inc.

foyd:glr

Gavin's Calc I Project 3, Fall 1997