Optimizing Fuel Cost for a Truck on a 400 Mile Trip

AI Thread Summary
The discussion revolves around calculating the fuel cost for a truck on a 400-mile trip, using the fuel consumption function G(x) defined as G(x) = (1/32)(64/x + x/50). Participants seek to derive the cost function C(x) based on this fuel consumption, with fuel priced at $1.60 per gallon. There is confusion regarding the variable x, which is clarified to represent speed in miles per hour, not distance. The main goal is to find both the cost function and the optimal speed for minimizing costs during the trip. The thread highlights a need for assistance in solving these mathematical problems.
ziddy83
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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
 
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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!
 
oh sorry...x represents miles per hour
 
How can i determine the cost function? Anyone?
 
nobody can help?
 

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