CPM Homework Help : CALC Problem 9-26

A square plot of land $100$ feet on each side is shown in the diagram at right. A pipe is to be laid in a straight line from point $A$ to a point $P$ on $BC$ , and from there to point $C$ . (Point $P$ cannot be point $B$ or point $C$ .) The cost of laying the pipe is $$20$ per foot if it goes through the lot from point A to point P (since it must be laid underground), and $$10$ per foot if it is laid along one of the sides of the lot. What is the most economical way to lay the pipe?

Hint:

Let $x = BP$ .
Now write expressions for $AB$ and $CP$ .
The function for the cost is $y = 20(AP) + 10(CP)$ .
Once you have written the cost function in terms of $x$ , differentiate and determine the value of $x$ that yields a minimum.

More Help:

$x ≈ 57.735$ ft
Note: This is not the answer to the question being asked.