Answer:
The ideal length is 16 feet
The ideal width is 8 feet
Step-by-step explanation:
The given parameters are;
The length of the fencing available to the homeowner = 32 feet
The number of sides of the rectangular chicken coup the fence will be applied = 3 sides
Let L represent the length and W, represent the width
Therefore, we have;
The perimeter of the fence = 2W + L = 32 feet
L = 32 - 2·W
The area is given by, A = Length, L × Width, W
A = (32 - 2·W) × W = 32·W - 2·W²
Differentiating with respect to W and equating to 0 to find the maximum point gives;
dA/dW = d(32·W - 2·W²)/dW = 0
32 - 4·W = 0
4·W = 32
W = 32/4 = 8
W = 8 feet
Given that the sign of the variable in the equation of the derivative is negative, the value we get is the maximum point
The ideal width W = 8 feet
The length, L = 32 - 2·W = 32 - 2 × 8 = 16 feet
Therefore, the ideal length, L = 16 feet.
