Let width = w Let length = l Let area = A 3w+2l=1200 2l=1200-3w l=1200-3/2 A=w*l A=w*(1200-3w)/2 A=600w-(3/2)*w^2 If I set A=0 to find the roots, the maximum will be at wmax=-b/2a which is exactly 1/2 way between the roots-(3/2)*w^2+600w=0 -b=-600 2a=-3 -b/2a=-600/-3 -600/-3=200 w=200 And, since 3w+2l=1200 3*200+2l=1200 2l = 600 l = 300 The dimensions of the largest enclosure willbe when width = 200 ft and length = 300 ft check answer: 3w+2l=1200 3*200+2*300=1200 600+600=1200 1200=1200 and A=w*l A=200*300 A=60000 ft2 To see if this is max area change w and l slightly but still make 3w+2l=1200 true, like w=200.1 l=299.85 A=299.85*200.1 A=59999.985
