Question

A rectangular field bounded on Side by a lake is to be fenced on 3 sides by 800 m of fence. What demensions wil produce a maximum area?

Answer 1

what formulas or functions would you use to develop relationships between side lengths?

Answer 2

2x + y = 800

xy = Area to maximize ...

Answer 3

using calculus:

A' = xy' + x'y

if we let A wrt/x, then x'=1

A' = xy' + y, this is min or max when A=0

0 = xy' + y

-y/x = y'

from P we get 2+y' = 0, so when y'=-2

-y/x = -2 ... or when y=2x

2x + 2x = 800; x = 800/4, y = 800/2