Optimizing Fuel Cost for a Truck on a 400 Mile Trip

In summary, the conversation is about a truck's fuel consumption and cost for a 400 mile trip. The cost function is being calculated using the function G(x) and the cost of fuel is assumed to be $1.60 per gallon. The question is posed about finding the speed that will result in the minimum cost for the trip. The conversation also briefly discusses the variable x and its representation as miles per hour. The individual is seeking assistance in determining the cost function.
  • #1
ziddy83
87
0
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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  • #2
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!
 
  • #3
oh sorry...x represents miles per hour
 
  • #4
How can i determine the cost function? Anyone?
 
  • #5
nobody can help?
 

Related to Optimizing Fuel Cost for a Truck on a 400 Mile Trip

1. What is a cost function?

A cost function is a mathematical equation that represents the relationship between the cost of producing something and the factors that affect it. It is commonly used in economics and business to help determine the most efficient way to produce goods or services.

2. Why is it important to find the cost function?

Finding the cost function allows us to understand the relationship between the cost of producing something and the factors that influence it. This information can help businesses make important decisions about production and pricing strategies, and can also help economists analyze the efficiency of different industries.

3. How do you find the cost function?

The process of finding the cost function involves collecting data on the cost of production and the factors that affect it, such as labor, materials, and overhead costs. This data is then used to create a mathematical equation that represents the relationship between these variables.

4. What are some common types of cost functions?

There are several types of cost functions, including linear, quadratic, and exponential. Linear cost functions have a constant rate of change, while quadratic cost functions have a curved shape. Exponential cost functions increase at an increasingly faster rate.

5. Can the cost function change over time?

Yes, the cost function can change over time as the factors that affect production costs change. This is why it is important to regularly analyze and update the cost function to accurately reflect the current economic and business conditions.

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