SOLUTION: A farmer wishes to make three equal sized rectangular corrals. The outside fence costs $3/ft and the inside fence costs $1/ft. If she has $1200 to spend on the corrals, what dime
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Question 737640: A farmer wishes to make three equal sized rectangular corrals. The outside fence costs $3/ft and the inside fence costs $1/ft. If she has $1200 to spend on the corrals, what dimensions will provide the corrals of greatest area? {All three are drawn right next to each other-picture three hersheys chocolate bars lined up long side by long side; the outside perimeter would be X (for the long edge) and Y (for the 3 short ends) Hope that helps and does not confuse.} Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A farmer wishes to make three equal sized rectangular corrals.
The outside fence costs $3/ft and the inside fence costs $1/ft.
If he has $1200 to spend on the corrals, what dimensions will provide the corrals of greatest area?
:
The fence consists of 3 widths and 2 lengths, one width will cost $1 a foot
the other two cost $3, as does the 2 lengths
:
3(2L) + 3(2W) + 1(W) = 1200
6L + 6W + W = 1200
6L + 7W = 1200
6L = 1200-7W
L =
:
Area = L * W
replace L
A = * W
A =
divide both coefficients by 6, write it as a quadratic equation
A = W^2 + 200W
Max area occurs on the axis of symmetry, find that with x =-b/(2a)
w =
using decimals here
w =
w ~ 85.7 ft is the width
Find the length
L =
do the math
L ~ 100 ft is length for max area for $1200
:
:
You should check this out for math errors
