The first thing we should do is write the functions.
For the area we have:
A = w * h = 20000 feet ^ 2
The price is:
Cost = (4 * 2 * h + 2 * 2 * w)
Substitute for h ::
C (w) = (4 * 2 * (20,000 / w) + 2 * 2w)
Rewrite we have:
C (w) = 160,000 / w + 4w
Take the derivative:
C '(w) = 160000 (-1 / w ^ 2) + 4
We equal zero and clear w:
0 = 160000 (-1 / w ^ 2) + 4
160000 / w ^ 2 = 4
w ^ 2 = 40000
w = 200 (approximately)
width = 200 ft; so cost is 2 * ($ 4) 200 = $ 1600
height = 20000/200 = 100 ft; so cost is 2 ($ 2) 100 = $ 400
Total cost = $ 2000
Answer:
The cost of the least expensive fence is:
Total cost = $ 2000
