posted by Taylor on .
A farmer needs to enclose three sides of a pasture with a fence (the fourth side is a river). The farmer has 42 meters of fence and wants the pasture to have an area of 220 sq-meters. What should the dimensions of the pasture be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)
If the width is w, then the length is 42-2w. So, the area is
y = w(42-2w)
y = -2w^2 + 42w
this is just a parabola, and y reaches its maximum when w = -42/-4 = 10.5
so, the pasture is 10.5 x 21. Area = 220.5
If we want just 220 m^2, then the field is 11x20