SOLUTION: MAx-Min word problem A farmer wants to make a rectangular corral along the side of a alrge barn and has enough materials for 60m of fencing. Only three sides must be fenced, sinc

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Question 175757: MAx-Min word problem
A farmer wants to make a rectangular corral along the side of a alrge barn and has enough materials for 60m of fencing. Only three sides must be fenced, since the barn wall will form the fourth side. What width of rectangle should the farmer use so that the maximum area is enclosed?
Answer by PTER(3) About Me  (Show Source):
You can put this solution on YOUR website!
x = width, y = length, A = area
2x + y = 60
y = 60 - 2x
 
A = xy
 
Substitute y = 60 - 2x.
A = xy
= x(60 - 2x)
= -2x^2 + 60x
 
Complete the square.
-2x^2 + 60x = -2(x^2 - 30x)
= -2(x^2 - 30x + 225) + 450
= -2(x - 15)^2 + 450
 
The maximum is 450 at x = 15.
 
The dimensions of the fencing should be 15m by 30m.