Question

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 400 m. of wire at your disposal what is the largest area that you can enclose, and what are its dimensions? Use the convention that length is longer than the width.

Answer 1

2x+y=400 A=xy area of farmland y=400-2x A=400x-2x^2 A'(x)= 400 -4x derivative of area with respect to x 0=400-4x find out where f ' equals 0 4x=400 x=100 A'(x)= 400 -4x A''(x)= -4 check 2nd derivative. if negative then relative max at x=100 2x+y=400 y=200 dimensions 100x200 hope it helped