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September 23, 2014

September 23, 2014

Posted by **Ass10** on Monday, November 14, 2011 at 3:17pm.

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 -
**Steve**, Tuesday, November 15, 2011 at 5:42amfigure 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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