Answer:
The maximum area is therefore is 93750 ft²
Step-by-step explanation:
The given parameter are;
The a]length of fencing available = 1500 ft.
The perimeter of the figure = 9·x + 4·y
Therefore, 9·x + 4·y = 1500 ft.
The area of the figure = 6 × (x × y) = 3·x × 2·y
From the equation for the perimeter, we have;
9·x + 4·y = 1500
y = 1500/4 - 9/4·x = 375 - 9/4·x
y = 375 - 9/4·x
Substituting the value of y in the equation for the area gives;
Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²
Area = 2250·x - 27/2·x²
The maximum area is found by taking the derivative and equating to zero as follows;
d(2250·x - 27/2·x²)/dx = 0
2250 - 27·x = 0
x = 2250/27 = 250/3
x = 250/3
y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5
The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²
The maximum area is therefore = 93750 ft.²
