For speeds between 40 and 65 miles per hour, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs $2.23 per gallon, and the driver is paid $15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck?
I would just like to know if I calculated this right...thanks!
C(S) ?= G/(480/S)
C(48) ?= G/(480/48)
C(48) ?= G/10
At 10 MPG, each mile costs 1/10 of a gallon of gas
P/S = PS^(-1), DS/DY(PS^(-1))=-1PS^(-2)
Min[F'(S)] @ 0=-P/S^2+G/480, solved for S
P/S^2 = G/480
S^2/P = 480/G
S^2 = 480P/G
For P=15.10 and G=2.23, we get S=SQRT(480*15.1/2.23)= ~57.011 MPG.