Find a function that models the total area of the two pens, Find the largest possible total area of the two pens

Question

Four thousand feet of fencing is used to enclose a rectangular area, which then is divided into two pens by placing fencing parallel to one side of the rectangle.

a) Find a function that models the total area of the two pens

b) Find the largest possible total area of the two pens

Answer 1

w represents the size of the three parallel sides

(4000 - 3w) / 2 represents the size of one length

A = w(4000 - 3w) / 2

A = (4000w - 3w²) / 2

A = 2000x - (3/2)w²

Maximum at -b / 2a, or w -2000 / -3