Freight Derivatives

In this project to study the effect of fuel prices and wages of drivers on the optimal driving speed for a truck driver. Analyze the realstionship between fuel costs and wages and speed 55 mph. Ur project is to determine how these variables affect the cost of freight. U are to determine whether there is a relationship to power optimal wage costs for most carriers which urges drivers to observe a speed limit of 55 mph.
Reading the study indicates that u in ideal conditions, an 18-wheeler gets 6 miles per gallon. fuel. The mileage is affected by the accelerated vehicle and its weight. The miles per gallon. decrease of .2 for each increase of £ 1,000. in the weight of the truck and 25,000 pounds of goods. In addition, the miles per gallon. decreases by .1 mpg. for each mph average truck over 45 mph.
a) Using this information, create an expression for the cost per mile of driving, taking into account only the salaries of pilots and fuel costs.

OK, this seems fun!

a)

You are given that the cost per mile has two components: wages of drivers (which will increase as speed decreases) and fuel costs (which will increase as speed increases).

Call the driver's hourly wage "dph (dollar salary per hour). We need to convert dollars per mile, so we will divide by the average speed of the truck (let's call it "mph" for miles per hour).

For example, if the pilot makes $ 10 an hour, an hour, it would be $ 10. And if he drove an average of 50 km / h at the same time, then he has traveled 50 miles. Therefore, the wage cost per mile is $ 10/50 miles = $ 0.20 per mile. We would get the same number this way: $ 10 per hour a· 50 miles / hour = $ 10/hour a— 1 mile = $ 0.20/mile hour/50.

Thus, the portion of wage calculation is dph / mph.

Now, for the cost of fuel. The cost of fuel is measured in units of dollars per gallon (call it "DPG" for the dollar per gallon), and we want units of dollars per mile. So we divide by the truck miles per gallon (call it "mpg" for miles per gallon).

For example, if gas is $ 2 a gallon and we used 10 gallons, which would have cost $ 20. And if the truck got 10 miles per gallon and we used 10 gallons, we traveled 100 miles. Thus, it would have cost us $ 20 for 100 miles, or $ 0.20 per mile. We get the same number by $ 2/gallon a· 10 miles / gallon = $ 2/gallon a— 1 mile = $ 0.20/mile gallon/10.

Thus, the fuel part of the equation will DPG / mpg.

Then the basic equation for the cost per mile of driving (in dollars per mile, or "DPM") will be:

dollar cost per mile = wages in dollars per hour and speed in miles per hour in fuel + dollars a gallon fuel / miles per gallon

or, using abbreviations / variables:

dpm = dph / DPG + mph / mpg

Now we have to figure in the rest of the information we provide.

They say the miles per gallon (mpg) is affected by two things: weight and speed (which we already call mph).

The best mpg for the truck is 6 miles per gallon, but it decreases by 0.2 miles per gallon for £ 1000 added more than 25,000 pounds. If we call the weight w, and measured in thousands of books, we can write that:

mpg = 6, if w <25
mpg = 6 - 0.2 (p - 25) = 6 - 0.2 W + 5 = 11 to 0.2 W, if w a‰¥ 25

The speed has a similar effect on mpg: mpg decreases 0.1 miles per gallon for each mile per hour over 45 mph. This can be written as:

mpg = 6 mph if <45
mpg = 6 - 0.1 (km / h - 45) = 6 - + 4.5 = 0.1 mph from 10.5 to 0.1 mph, if a‰¥ 45 mph

If both things are true (the vehicle is over 25,000 pounds and the speed exceeds 45 mph), the mpg will be:

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