Posted by **nancy** on Tuesday, April 24, 2007 at 3:10am.

A small truck is to be driven 300 miles on a freeway at a constant speed of x miles per hour. Speed laws on the freeway require that a truck must be driven between 30 miles per hour and 70 miles per hour. assume that fuel cost $3.50 per gallon. in addition, assume that for a given speed of x miles per hour, fuel is consumed at the rate of 1+(x^2/600) gallons per hour. If the salary of the driver is based on $20 per hour, how to find the most economical speed of the total cost of the trip? plz help!

Write the cost function:

C=20t + 3.50(1+(x^2/600)) gives cost as a function of time and speed. But distance, is related to speed x and time, so time= distance/speed or

Cost= 20 *300/x + 3.50(1+(x^2/600)) so now cost is a function of speed.

minimize cost as a function of speed (set first derivative equal to zero).

check my math.

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