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

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

## Answer this Question

## Related Questions

- Calculus - You are the owner of a delivery company with one truck. The trucks ...
- Calculus/ Optimization - A truck driver, on assignment from the owner of the ...
- Math/ Calculus Please HELP!!! - A truck driver, on assignment from the owner of ...
- math - Your Porsche's gas mileage (in miles per gallon) is given as a function M...
- calculus - 16. Given the following information, determine the constant speed, ...
- calculus - 16. Given the following information, determine the constant speed, ...
- Math - A small truck is to be driven 300 miles on a freeway at a constant speed ...
- math for the office professional - one of your delivery trucks traveled 1,200 ...
- statistics - 16. Based on tests of the Chevrolet Cobalt, engineers have found ...
- Algebra - The fuel efficiency for a certain midsize car is given by E(v) = &#...

More Related Questions