Writing for Mathematics (Math 300) Blok Fall 2003

Essay 3¹


In this essay you are to prepare a report for the Interstate Trucking Board on the effects of the price of fuel and drivers’ wages on a trucker’s optimal driving speed. The members of the board all have a college education, and have taken calculus, but their memory needs to be refreshed. So when you are finding an optimal value for a variable, explain briefly what method you are using, and why it works.

The report is based on an extensive study commissioned by the Board. The study showed that the primary variable expenses for any over-the-road freight hauler are the wages for the driver and the cost of fuel. The study found that maintenance and replacement costs for vehicles, although considerable, did not vary significantly from carrier to carrier. On the other hand, the fuel costs and wages did vary. Your report is to explain how these two variables affect the cost of transporting freight. In particular, your report should suggest possible measures that will encourage freight carriers to get their drivers to abide by the 55 mph speed limit.

The study found that, under ideal conditions, an interstate freight hauling vehicle (18 wheeler) has an efficiency of 6 miles per gallon of fuel (6 m/g). This mileage is affected by the speed of the vehicle and by its weight. In general, the efficiency decreases by 0.2 m/g for every increase of 10,000 lbs in the weight of truck and freight over 30,000 lbs. Also, the efficiency decreases by 0.1 m/g for each mile per hour the truck averages above 45 m/h.

The following should be included:

a) Create an expression for the cost per mile of driving, taking into account only the driver’s wages and the fuel cost.

b) Suppose that the national average for diesel fuel is $1.50 per gallon, that drivers earn on the average $20 per hour, and that the average weight of a loaded truck is 80,000 lbs. What is the optimal average speed under those conditions?

c) Compute the cost per mile at an average speed of 55 and 60 m/h. Discuss the pros and cons for the freight company of abiding with the speed limit when hauling produce from California to Chicago.

d) In a) - c) you set up an equation relating cost per mile, fuel cost, wages, weight of the truck, and the average speed of the truck. This equation is a mathematical model of interstate freight hauling costs. Using this model, determine the fuel cost that makes 55 m/h the optimal average speed for trucking companies.

e) Each year drivers’ wages change as a result of negotiations and inflation. The cost of fuel also fluctuates, but can be adjusted by surcharges and fuel taxes. Thus the relationship between wages and fuel the cost of fuel can be altered by various government agencies. Assuming that 80,000 lbs remains the national average for the weight of a truck (including freight), what should be the relationship between fuel cost and wages to maintain 55 m/h as the optimal speed?





An outline for this essay should be handed in class on Wednesday 11/5. The outline will be returned on 11/12. The first draft is due on 11/19, and the final version on 12/3.

On the outline:

It is important to have a clear understanding of what you want a reader to get out of your essay, and your outline should already convey this. A few points that may help:

1. Include a title which is instructive.

2. The introduction should reflect a clear idea of the purpose of the essay: what it intends to convey, to whom, and in what setting.

3. The points of the body should be ordered in a logical way, and in one which will hold the attention of the reader. Describe each of them briefly; be specific enough so that someone reading the outline will have a rough understanding of their purpose. If you use sections and subsections, list them with their proposed headings, and describe briefly their content.

4. Do not introduce new material in your conclusion.

¹ The essay topic is adapted from a project in “Calculus”, by Hughes-Hallett, Gleason, and McCallum (3rd edition), John Wiley and Sons, Inc., which in turn is adapted from L. C. Leinbach, “Calculus Laboratories Using Derive”, Wadsworth, 1991.