A developer wants to enclose a rectangular grassy lot that b

A developer wants to enclose a rectangular grassy lot that borders a city street parking. If the developer has 280 feet of fencing and does not fence along the street, what is the largest area that can be enclosed.

Solution

let length of grassy lot = l

width = w

only 3 sides are to be fenced

l + 2w = 280

l = 280 - 2w

area = l * w

area = (280 - 2w ) * w

= 280 w - 2w^2

maximum area occurs at w = -280 / -2(2) = 70

hence , maximum area = 280 (70 ) - 2 (70)^2 = 9800

largest area enclosed = 9800 square feet