SOLUTION: A farmer has a 150m fencing wire to set up around a rectangular lot beside a river for his ducks and geese. If a 10m opening in the side of the river is left, what would be the len

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Question 636491: A farmer has a 150m fencing wire to set up around a rectangular lot beside a river for his ducks and geese. If a 10m opening in the side of the river is left, what would be the length and width for maximum areas?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A farmer has a 150m fencing wire to set up around a rectangular lot beside
a river for his ducks and geese.
If a 10m opening in the side of the river is left, what would be the length
and width for maximum areas?
:
Let L = outside length
then
(L-10) = river length
and
W = the width
:
total fence equation
L + (L-10) + 2W = 150
2L + 2W = 150 + 10
2L + 2W = 160
Simplify, divide by 2
L + W = 80
W = (80-L)
:
Area = L * W
Replace W with (80-L)
A = L(80-L)
A = -L^2 + 80L
A quadratic equation, max area will be the axis of symmetry x=-b/(2a)
In this equation: a=-1; b=80
L = %28-80%29%2F%282%2A-1%29
L = 40 m, length for max area
then
W = 80-40 = 40m width for max area
:
40m by 40m for max area (1600 sq/m)