# Optimization Problem?

A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 16 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.

Please Help!

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- SumDudeLv 72 months ago
Help yourself. Draw a picture and puzzle through it manually, then learn the formula(s) you would use whenever you encounter this situation. P S A half-circle would actually provide the most enclosed area.

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- davidLv 72 months ago
A = lw

let l = r --- the riverbank .. which has one parallei side to be fenced

16 = r + 2w

r = 16 - 2w

A(w) = w(16- 2w) = 16w - 2w^2

A' = 16 - 4w = 0

w = 4 km

l = 16 - 2*4 = 8km

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