SOLUTION: A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs $30 per foot, and material

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Question 490575: A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs $30 per foot, and material for the other two sides costs $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular garden bounded on one side by a river is to be fenced on the other three sides.
Fencing material for the side parallel to the river costs $30 per foot, and material for the other two sides costs $10 per foot.
What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
:
the total cost for three fenced sides
30L + 10(2W) = 1200
30L + 20W = 1200
simplify divide by 10
3L + 2W = 120
2W = 120 - 3L
W = %28120-3L%29%2F2
W = (60-1.5L)
:
A = L * W
replace W
A = L(60-1.5L)
A = -1.5L^2 + 60L
to find max area, find the axis of symmetry; x = -b/(2a)
L = %28-60%29%2F%282%2A-1.5%29
L = %28-60%29%2F%28-3%29
L = + 20 ft is the length
Find the width
W = 60 - 1.5(20)
W = 30 ft the width
then
max area for $1200, 20 by 30 ft
:
:
Check this finding the cost for the perimeter with these dimensions
30(20) + 10*2(30) =
600 + 600 = 1200