A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $12 per foot and on the other three sides by a metal fence costing $4 per foot. I

Question

If the area of the garden is 1250 ft², find the dimensions of the garden minimizing the cost. (Let x be the length of the brick wall and y be the length of an adjacent side in feet.)

Answer 1

Area = 1250 = xy --> y = 1250/x

Cost = 2(4)y + 4x + 12x = 8y +16x = 8(1250)/x + 16x

C'(x)= -8(1250)/x² + 16

Set C'(x) to zero and solve for x

16x² = 8(1250)

x² = 625

x = 25 feet

y = 1250/25 = 50 feet