Question

Abc daycare wants to build a fence to enclose a rectangular playground. the area of the playground is 930 square feet. the fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of brick, costs $20 per foot. find the length of the brick fence that will minimize the cost of enclosing the playground. (round your answer to one decimal place.)

Answer 1

xy = 940

and

Cost = 5(2x) + 5y + 10y (I chose y to be the side with brick). The cost equation simplifies to:

C = 10x + 15y

Replace y in the cost equation with 940/x:

C = 10x + 15(940/x)

C = 10x + 14100/x <---this is the equation you need to minimize.

C' = 10 - 14100/x^2

10 - 14100/x^2 = 0

14100/x^2 = 10

x^2 = 14100/10 = 1410

x = sqrt(1410) = 37.55

y = 25.03 <---this is the length of the brick fence.