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You are the owner of a delivery company with one truck. The trucks fuel economy is 1200/x miles per gallon when driving at x miles per hour (where 80 >= x <= 110). The price of fuel is $1 per gallon. You pay the truck driver $8 per hour.
If a delivery 100 miles away is planned, at what speed between 80 and 110 mph should the truck to drive to minimize the cost of the trip?

I'm having trouble finding the equation to differentiate.
Please show work.

  • Calculus -

    figure the cost of the trip: driver pay + fuel cost

    if it's 100 miles, and the driver drives at x miles/hr, then the trip takes 100/x hours.

    fuel used is x/1200 gal/mi * 100 mi

    cost = 8 * 100/x + 1 * 100 * x/1200

    Looks like dcost/dx = 0 at about x=97mph
    Good luck finding a highway with that speed limit!

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