A farmer is planning to put in a garden next to his barn. He is planning to fence in the garden on three sides (the barn will make the fourth side). He has 100 feet of fencing to use. Find an equation for the area of the garden. Explain/Show work.

L + 2W = 100

L = 100 -2W

W ( 100 - 2W ) / area covered by fence

- 2w^2 + 100 W / maximum area covered

f( w ) = - 2 w ^2 + 100w

f( w ) is maximum value at w = -100/ -4 = 25 ft

Maximum area of garden is a square with side = 25 ft