Minimize fuel cost for a 400-mile trip with consumption G(x)

[ziddy83]

I was wondering if anyone can help me on this problem...

A truck burns fuel at the rate of G(x) gallons per mile. Where

$$G(x) = \frac {1} {32} \left(\frac {64}{x} + \frac {x}{50} \right)$$

a. Find the cost function C(x) if the truck takes a 400 mile trip. Assume that the cost of fuel is $1.60 per gallon.

b. What is the speed that will produce minimum cost on this trip?

So...if anyone can help me with this...Please..please do so, I would be very very appreciative. Thanks

 

[HallsofIvy]

What does x represent?


At first I thought it was the distance which makes (a) easy but then (b) makes no sense. Is x the speed? No, that way (a) makes no sense!

 

[ziddy83]

oh sorry...x represents miles per hour

 

[ziddy83]

How can i determine the cost function? Anyone?

 

[ziddy83]

nobody can help?