# Thread: (minimum/maximum problem) Minimum price for gasline

1. ## (minimum/maximum problem) Minimum price for gasline

Hi all!

I have the following math problem to be solved, and I really can't find it

"A gasline has to be put from the coast to the city, begin and endpoint are determined. The costs along the coast are 750 dollar / kilometer, and through the city 1250 dollar / kilometer. Give the function to determine the minimum price - also give the minimum price."

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2. ## Re: (minimum/maximum problem) Minimum price for gasline

Originally Posted by zerox
Hi all!

I have the following math problem to be solved, and I really can't find it

"A gasline has to be put from the coast to the city, begin and endpoint are determined. The costs along the coast are 750 dollar / kilometer, and through the city 1250 dollar / kilometer. Give the function to determine the minimum price - also give the minimum price."
I assume the distance "x" is along the coast.

let C(x) be cost as a function of x

$C(x) = 750x + 1250\sqrt{120^2 + (160-x)^2}$

find C'(x) and minimize

3. ## Re: (minimum/maximum problem) Minimum price for gasline

Great, thank you!

May I ask how you came to this solution? I have been staring at the picture for quite a while and failed to understand how to solve it.

4. ## Re: (minimum/maximum problem) Minimum price for gasline

Originally Posted by zerox
Great, thank you!

May I ask how you came to this solution? I have been staring at the picture for quite a while and failed to understand how to solve it.
I didn't solve the problem ... just set it up.

the expression for the length of the line through the city was determined using Pythagoras.