Where Should You Study?

Introduction

Where should you study? For a minimum of distractions, you should study in the library.

But where in the library?

I once worked at a college whose science library had a mezzanine floor with a row of study desks beneath and parallel to a row of ceiling fluorescent light fixtures ("lights").

Put yourself in the shoes of a mathematics student choosing a desk on the mezzanine:

You prefer a well-lighted desk. Your first inclination is to pick a desk directly under a light.

But then as you break off from your 17th daydream over an assignment in your mathematical modeling course, you see another student from your class come in, size up the lighting situation, and choose a desk situated directly between two light fixtures!

Does she know something that you don't?

In fact, it is beginning to seem to you that maybe there is more light on her desk. . . .

Realizing that the amount of light is inversely proportional to the square of the distance from the source (it's a good thing you took physics!) and assuming that the light radiates equally in all directions from a fluorescent bulb that can be considered a point source (your instructor in mathematical modeling insists that yo umake explicit any assumptions that you make in setting up a problem), you decide to interrupt your other work and set out to calculate the amount of light at each point along the row of desks.

Since you are interested in maximizing light, you know that the optimizationtechniques that you learned in calculus are likely to come in handy.