SOLUTION: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. If the area of
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Question 1140031: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 122 square feet, find the dimensions of the garden that minimize the cost. Found 2 solutions by math_helper, ikleyn:Answer by math_helper(2461) (Show Source):
L*W = 122 (1)
Cost equation:
C = 20L + 10L + 10W + 10W
C = 30L + 20W (2)
Eq (1) --> L = 122/W
Substitute for L in (2):
C = 30*(122/W) + 20W
C = 3660/W + 20W
Differentiate WRT to W:
dC/dW = -(3660/W^2) + 20
Set the derivative to 0:
-(3660/W^2) + 20 = 0
20W^2 = 3660
W^2 = 183
W = ft
L = 122/13.52775 = ft
[ min(C) = $541.11 for these dimensions ]
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