A truck gets 10 miles per gallon (mpg) of diesel fuel traveling along an interstate highway at 50 mph. This mileage decreases by 0.15 mpg for each mile per hour increase above 50 mph.

(a) If the truck driver is paid $30/h and diesel fuel costs P = $3/gal, which speed v between 50 and 70 mph will minimize the cost of a trip along the highway? Notice that the actual cost depends on the length of the trip, but the optimal speed does not.
(b) Plot cost as a function of v (choose the length arbitrarily) and verify your answer to part (a).
(c) Do you expect the optimal speed v to increase or decrease if fuel costs go down to P = $2/gal? Plot the graphs of cost as a function of v for P = 2 and P = 3 on the same axis and verify your conclusion.