Question

Abc daycare wants to build a fence to enclose a rectangular playground. the area of the playground is 910 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 $15 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

Given that the area of the playground is 910 square feet, let the length of the playground be x, then the width of the playground is given by
`(910)/(x)`

Given that 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 $15 per foot. Let the side with the brick fence be the side which measures x feet.

Then the cost for fencing the entire playground is given by


`C=5\left( (910)/(x) \right)+5x+5\left( (910)/(x) \right)+15x= (9100)/(x) +20x`

For, minimum cost,


`(dC)/(dx) =0 \\ \\ \Rightarrow- (9100)/(x^2) +20=0 \\ \\ \Rightarrow20x^2-9100=0 \\ \\ \Rightarrow x^2-455=0 \\ \\ \Rightarrow x=\pm√(455)`

But x can't be negative.

Therefore, the length of the brick fence that will minimize the cost of enclosing the playground is 21.33 feet.