Problem+5+Meredith

excellent! (ms sweeney)

The objective function is the equation for Area, or A=LW, which we are supposed to maximize

Perimeter = 2L + 2W 100 = 2L + 2W L=50-W Area = LW Area = (50-W)W Area = 50W-W²

To find absolute maximum: A'=50-2W 0 = 50-2W W = 25

A'' = -2, so the graph is always concave down (meaning the critical value at W=25 must be a local maximum) lim x-->∞ = -∞ lim x--> -∞ = -∞

The end behavior indicates that there is an absolute maximum at W=25 If W=25 then L=25, so the dimension must be 25x25