Recently, I received a request from a local window manufacturer for help in determining the dimensions of a window to be manufactured for a trapezoidal rough opening in a house under construction. The rough opening dimensions were known, as well as the...
Since the publication of the first edition of Samuelson's Principles text in 1948, introductory treatments of the short-run macroeconomic issues of inflation and unemployment have been based on the Samuelson-Cross model [Samuelson 1985, 122- 1881. This...
We are interested in modeling the length of tenure in office of a legislator. Once he or she is initially elected, the number of consecutive terms served depends on many factors and may be regarded as a random variable. Inherent random fluctuations can...
I was recently asked by a chemist to figure out the scheme used to create the bar code for the extended zip code on business reply mail. With a half dozen samples to experiment with, this puzzle took a few hours to solve. Not unexpectedly, the code is...
The study of atonal music might seem far removed from mathematics, but in fact a close bond exists. Moreover, a good deal of the relevant mathematics can be understood by those with a knowledge of elementary algebra. The purpose of this article is to...
For centuries people have wished to communicate with one another while keeping their communications secret from outsiders. In order to accomplish this, the sender of a message must disguise it before sending it. The process of disguising a message is...
A process whose stages are governed by the initial state the process was found in is known as a Markov process. The study of such processes leads to many applications, among them the analysis of the length of the World Series. In this paper we will...
Many administrators experience the feeling that the amount of paperwork they need to deal with increases substantially through time; that the number of difficult problems that need to be dealt with never diminishes no matter how fast one solves them....
Shuttle's Robot Arm Snares Errant Satellite [Wilford 1984al; Robot Arm Knocks Troublesome Ice Off Space Shuttle [Wilford 1984bl. These are headlines which appeared on newspaper articles about space shuttle flights. The orbiter, which is the plane-like...
An employer is seeking a new secretary. Under a rather rigid hiring procedure, the employer is allowed to interview n candidates one at a time and decide, at the conclusion of each interview, whether or not to hire that applicant. If the employer...
Producers and consumers of products are interested in knowing how long items will function before failure. Producers need to know the time-to-failure of their products in order to control the manufacture of them. Consumers need to be assured that the...
Early in our mathematical modeling course, Penelope Smith, the student co-author, fulfilled her library research assignment by investigating existing models of fire evacuation. Although there were a few studies of evacuating adults from public...
One of the most widely used sources of problems for a mathematical modeling course is the series of modules prepared by the TEAM project at Oklahoma State University and distributed by the Mathematical Association of America. The module on Highway...
The classic inventory problem asks how many items should be made per batch to minimize the total costs of production. This problem can be presented as soon as beginning calculus students learn the definition of the derivative, and it provides a...
The world of computing stands at the brink of what may be a revolution, the use of parallel processing to speed up calculations that take too long on a conventional computer. Parallel processing involves many processors working somewhat independently...
Consider the following scenario. You go to the supermarket and select 11 items. Upon reaching the checkout area, you notice that the express line is for customers with 10 items or fewer, while the non-express lines are quite long. You have several...
On June 2, 1987, the Los Angeles Lakers and the Boston Celtics met in Los Angeles for the first game of the 1987 National Basketball Association championship series, with the Lakers heavily favored to win the series. The posted odds in advance in...
Many health insurance policies carry a deductible. It is the amount below which the insurance company has no responsibility. Only claims above this deductible amount will be compensated by the insurance company. There are two general types of...
Recently Michael RRed criticized the calculus curriculum for teaching how to differentiate functions of the form f (z)g() without providing any real applications [Reed 19871. Without endorsing Reed's sentiment, we present an everyday application of...
We discuss a class of linear programming minimization models known as cutting stock, trim loss, or bin packing models. Specifically, we compare the results of applying two such models to the problem: Given certain stock lengths, how should the stocks...