CPM Homework Help : CALC3RD Problem 9-25

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 side $\overline{BC}$ , and from there to point $C$ . (Point $P$ cannot be point $B$ or point $C$ .) The cost of laying the pipe is $$20$ per foot if the pipe goes through the lot from point $A$ to point $P$ (since it must be laid underground) and $$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?

Square, A B C D, with point, P, on side, B C, about 1 fourth of the way from B to C, bold segments from, A to P, & from P to C.

Hint:

Let $x = \overline {BP}$ .
Now write expressions for $\overline{AB}$ and $\overline{CP}$ .

More Help:

The function for the cost is $y = 20(\overline{AP}) + 10(\overline{CP})$ .

More Help:

Once you have written the cost function in terms of $x$ , differentiate and determine the value of $x$ that yields a miniumum.

Partial Answer:

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