# Thread: [SOLVED] Minimize the total construction costs

1. ## [SOLVED] Minimize the total construction costs

A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs 1.7 times as much money to lay pipe in the water as it does on land, how far down the shoreline from P should the pipe from the island reach land in order to minimize the total construction costs? I cannot figure out an equation for this problem that i will be able to use to find the derivative then set equal to 0 and solve for x to get the minimal cost =( Any help would be great. thank you

2. Have you drawn a picture? Then which bit are you going to label x in order to get these expressions? ...

10 - x

$\displaystyle 1.7 \sqrt{6^2 + x^2}$

And what are they? (Sorry, did that say solved already...)

3. Yeah it did haha, but thank you. i did use what you just posted and i got the correct answer. thanks again =)