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?

Question

amistre64 · Answer

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

amistre64 · Answer

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2x + y = 800

xy = Area to maximize ...

amistre64 · Answer

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