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

Quote:

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

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

find C'(x) and minimize

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.

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

Quote:

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.