A landscape architect wishes to enclose a rectangular garden on one side by a brick wall

Question

A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $27 per foot and on the other three sides by a metal fence costing $9 per foot. If the area of the garden is 200ft^2 find the dimensions of the garden minimizing the cost.

(Use decimal notation. Give your answers as whole or exact numbers.)

Answer 1

x y = 200

y = 200 / x

C = 27 x + 9 ( x + 2 y )

C = 36 x + 18 y

C = 36 x + 18 (200 / x )

C = 36 x + 3600 / x

C’ = 36 - 3600 / x ^ 2

36 x ^ 2 = 3600

x = 10. y = 200 / x

y = 200 / 10 = 20