A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $50/ft and on the other three sides by a metal fence costing $40/ft. If the area of the garden is 88 square feet, find the dimensions of the garden that minimize the cost.

Answer 1

length of garden ==== x ft
width of garden ===== y ft
xy = 88
y = 88/x

Cost = 50x +40(2y + x)
= 50x + 40x + 80y
= 90x + 80(88/x) = 90x + 7040/x

dCost/dx = 90 - 7040/x^2 = 0 for a min cost
90 = 7040/x^2
90x^2 = 7040
x^2 = 704/9
x = √704/3 = 8√11/3 ft = appr 8.844 ft
y = 88/8.844 = appr 9.95 ft

Answer 2

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