Answer:
31.6 feet by 15.8 feet.
Step-by-step explanation:
Area of a Rectangle = Length X Breadth = LB
The area of the playground is to be 500 square feet
Therefore:
LB=500
Perimeter of the Rectangle = 2(L+B)
The Chain link fence that costs $2 per linear foot on three sides and a fancier wooden fence that costs $6 per linear foot on the fourth side.
Cost = ${2(L+2B)+6L}=2L+4B+6L=8L+4B
Cost= $(8L+4B)
From: LB=500, B=500/L
Substitute B into 8L+4B
C(L) =
C(L)=
The minimum cost of the fencing occurs when the dimensions are minimum.
If we take the derivative of C(L)
At
Recall: B=500/L
The dimensions that minimizes the total cost of the fencing are 31.6 feet by 15.8 feet.