Answer:
10,416.67 ft²
Step-by-step explanation:
If the length of the three parallel partitions is h, and the width of the two parallel walls is w, then the perimeter is:
500 = 3h + 2w
The area is:
A = hw
Solve for w in the first equation:
2w = 500 − 3h
w = 250 − 1.5h
Substitute into the second equation:
A = h (250 − 1.5h)
A = 250h − 1.5h²
We can find the maximum using vertex of a parabola:
h = -b / (2a)
h = -250 / (2 × -1.5)
h = 83.33
Or using calculus:
dA/dh = 250 − 3h
0 = 250 − 3h
h = 83.33
Therefore, the maximum area is:
A = 250h − 1.5h²
A = 10,416.67
