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A truck driver, on assignment from the owner of the truck is to drive on a 300 mile stretch of highway at a constant speed of v miles per hour. According to road signs, the minimum speed allowed is 55 miles per hour and the speed limit is 70 miles per hour. The cost of gas on the day of the trip is \$2.60 per gallon and the gas in the truck has been measured to consumed at a rate of (1+(1/400))*(v^2) gallons per hour.

If the truck driver earns \$20 per hour what speed v should the truck driver be assigned to drive in order to keep the cost for the owner of the company as low as possible? Find the minimum cost and compare it to the cost when the driver drives at 55 and 70 miles per hour

• Math/ Calculus - typo -

I think you have a typo in the gas consumption expression. As it stands, why not just express it as (401/400) v^2?

Anyway, the trip takes 300/v hours to drive.
the cost for the driver is 20*300/v for driving time

the cost of gas is 2.60*(gals/hr)(300/v)

add them up, plug in values for v, and find where dc/dv=0 for minimum cost.

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