ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 900 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 $10 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.)

Question

Reiny · Accepted Answer

let the length of the side using bricks be x ft
let the other two sides each be y ft

given: xy = 900 --> y = 900/x

cost = 5(x + 2y) + 10x
= 15x + 10y
= 15x + 10(900/x)
d(cost)/dx = 15 - 9000/x^2
= 0 for min of cost
15 = 9000/x^2
15x^2 = 9000
x^2 = 600
x = √600 = 10√6 = appr 24.5 ft

check my arithmetic

Anonymous · Answer

a 5 foot fence will be built around the perimeter of a 50 foot by 120 foot rectangular lot. if the fence costs $1.80 per linear foot for labor and $.40 per square foot for material, what will be the cost of the fence?

Tomas · Answer

I need the area not the perimeter.