DEFINE the function l ( w ) to represent the length of the field as a function of the width.

Question

1. Mr. Darcy wants to fence in a rectangular area of his field using 1400 feet of fence he already has. He wants the area to have three fenced off congruent sections for each of his three horses. (A fence will run down all of the lines you see in the drawing.) He wants to maximize the area of the field in order to give his horses the most pasture possible while keeping them separate. 

Answer 1

length of fencing = 1400 = 2l + 4w

Area is maximized when length = width (with fixed amount of fencing)

1400 = 2w + 4w

1400 = 6w

w = 233.33 ft