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?

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