1. ## Optimization

A rectangular plot is to be fenced in using the side of an existing barn that is 50 feet long as one side of the plot. Two hundred feet of fencing are available for the other 3 sides of the plot. Find the largest possible area that can be enclosed.

2. Originally Posted by Reefer
A rectangular plot is to be fenced in using the side of an existing barn that is 50 feet long as one side of the plot. Two hundred feet of fencing are available for the other 3 sides of the plot. Find the largest possible area that can be enclosed.
Draw the rectangle. Extend one of the sides to indicate "an existing barn" on that side. Label that side, and the opposite side, as "L", noting that L must be no more than 50. Label the two remaining sides as "w".

Note that the fencing indicates the fenced perimeter; the side with the barn will not be counted in this perimeter, so 2w + L = 200.

Solve for L in terms of w. Plug the result into the "area" formula for a rectangle.

Maximize the area, keeping the limits on L in mind. :wink: