Question

Sam has 1200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Express the area of the field as a function of its dimension. Find the dimensions of the field that has the largest area.

Answer 1

length parallel to river --- x ft
each of other two sides -- y ft

2x + y = 1200 ----> y = 1200 - 2x

area = xy
= x(1200-2x)
= 1200x -2 x^2

since you labeled it "Calculus"
d(area)/dx = 1200 - 4x
= 0 for a max of area
4x = 1200
x = 300

width = 300
length = 1200 - 2(300) = 600