Expert: Cody Thompson - 4/11/2007

Question
A man wants to build a rectangular enclosure for his herd. He only has $900 to spend on the fence and wants the largest size for his money. He plans to build the pen along the river on his property, so he does not have to put a fence on that side. The side of the fence parallel to the fence will cost $5 per foot to build, whereas the sides perpendicular to the river will cost $3 per foot.What dimensions should he choose?


Answer
Hello Chris:

The perimeter of the fence is l+2w. The parallel side has cost $5 per foot so we have 5l. The perp sides to the river have cost $3 per foot, so we have 3*2w.

The cost is then 5l+6w=900...........[1]

Area is l*w...........[2]

Solve [1] for, say, l:

l=(900-6w)/5

Sub into [2] and simplify:

180w-((6w^2)/5)

Differentiate and get: 180-(12w/5)

Set to 0 and solve for w and get w=75

Plug this back into the equation above and we find l=90

So, his dimensions are 90 by 75.


Does this help?.

Take care,
Cody