A Truck get 10 miles per gallon of diesel fuel traveling along an interstate highway at 50mph. This mileage decreases by 0.15 mpg for each mile per...

A Truck get 10 miles per gallon of diesel fuel traveling along an interstate highway at 50mph. This mileage decreases by 0.15 mpg for each mile per hour increase above 50 mph. The truck driver is paid $30 per hour, and diesel fuel costs P= $3 per gallon. Assume the truck travels a trip of length L at a speed of v mph. Establish a function definition for C(v), the total cost of the trip. Then use calculus and the first derivative to determine which speed v between 50-70 mph will minimize the cost of a trip along the highway. Show all of your work. (Notice that the actual cost depends on the length of the trip, but the optimal speed does not.)