The number of miles, per gallon of fule, that can be traveled by an interstate f

Question

The number of miles, per gallon of fule, that can be traveled by an interstate freight hauling truck (an 18 wheeler) depends on both the speed of the truck and its weight, as follows: start with a base of 11 miles per gallon, then subtract 0.1 times the truck's average speed, and then subtract 0.00002 times the total weight of the truck. So, the fuel efficiency decreases as the truck's speed increases, and the fuel efficiency decreases as the weight of the truck and its cargo increases. As an example, note this formula yields an average efficiency 6 miles per gallon for a 25,000 pound truck travelling at 45 mph.

Using this information, create an expression for the cost per mile of driving, taking into account only the two factors: the driver's wages and the fuel cost. Your equation should relate total cost per mile depending on driver's hourly wage, his/her average speed, price of fuel, and weight of the truck. This equation is a mathematical model of interstate freight hauling costs.

Explanation / Answer

solution:

suppose the speed of truck is s and weight of truck is w

then the total distance per unit fuel will be

T(s,w)= 11-0.1s-0.00002w

now this is the total distance travelled per unit fuel

if x gallon fuel burnt then

total distance travelled T=

( 11-0.1s-0.00002w)x

now

if price of fuel is z per gallon and driver daily wage is r dollar per hour and he drives for t hours then total cost

C= [( 11-0.1s-0.00002w)xz] + rt

and cost per mile

C/T=[( [( 11-0.1s-0.00002w)xz] + rt)/(( 11-0.1s-0.00002w)x)]

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