Optimization, Minimization Calculus Problem--I'm Stuck!

The problem I'm working on is...

A truck gets 500/*x*

miles per gallon (mpg) when driven at a constant speed of *x mph, where 40 ≤ x ≤ 80.*

If the price of fuel is $2.80/gal and the driver is paid $20/hr, at what speed is it most economical for the trucker to drive?

I have been searching for similar problems in my text book and class notes but am unable to find one. I'd greatly appreciate any help or similar examples!

Thanks!

Re: Optimization, Minimization Calculus Problem--I'm Stuck!

The trick of it is to find what you want to optimize. In this case it would be miles per dollar.

You are given miles/gallon, dollars/gallon, miles/hour, and dollars/hour.

Your equation will be made up of two pieces, your fuel miles/dollar and your driver's miles/dollar. The sum of these will create your total miles/dollar.

Once your equation is set up it is straight forward optimization.