Optimizing Fuel Cost for a Truck on a 400 Mile Trip

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Homework Help Overview

The discussion revolves around optimizing fuel costs for a truck on a 400-mile trip, focusing on a fuel consumption function G(x) that depends on speed x, measured in miles per hour. Participants are tasked with finding a cost function C(x) based on this fuel consumption and the cost of fuel.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the variable x, with initial confusion about whether it represents distance or speed. Questions about how to derive the cost function from the given fuel consumption function are also raised.

Discussion Status

The discussion is ongoing, with some participants seeking clarification on the definitions and implications of the variables involved. There is a lack of explicit consensus on the approach to take, but participants are engaging with the problem and asking relevant questions.

Contextual Notes

There is a specific focus on the relationship between speed and fuel consumption, and the cost of fuel is fixed at $1.60 per gallon. The problem context includes a 400-mile trip, which may impose constraints on the solutions being considered.

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

[tex]G(x) = \frac {1} {32} \left(\frac {64}{x} + \frac {x}{50} \right)[/tex]

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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