The problem statement, all variables and given/known data We have to solve this problem using only what we learned in calculus (no linear programming) I attached a picture to help :) A farmer wants to build a rectangular pen. He has a barn wall 40 feet long, some or all of which must be used for all or part of one side of the pen. In other words, with f feet of of fencing material, he can build a pen with a perimeter of up to f+40 feet, and remember he isn't required to use all 40 feet. What is the maximum possible area for the pen if 100 feet of fencing is available? The attempt at a solution I attempted to solve by finding the critical points of the derivative: 2x+y=100 --> y=100-2x x(100-2x)=100x-2x^2 f'(x)=100-4x 100-4x=0 --> x=25 2(25)+y=100 --> y=50 A=1250 BUT I realize this is wrong because if y=50, then the side of the barn needs an extra 10 feet, but all of the fencing material has been used by the other 3 sides. Help please?