Question

Rancher juan wants to enclose a rectangular area beside a river. there are 240 yards of fencing available. what is the largest total area that can be enclosed?

Answer 1

Perimeter = 2L + 2W →  240 = 2L + 2W  →  120 = L + W  → 120-L = W
Area = L x W  → Area = L(120-L)  →  Area = 120L - L²
Find the derivative: dA/dL = 120 -2L → 0 = 120 - 2L → L = 60

Area = 120L - L² = 120(60) - (60)²  = 7200 - 3600 = 3600

The maximum area is 3600 yds²