let b be the dimension opposite the building and s be the dimension of the sides, and m be the amount of material used...
m=b+2s
b=m-2s
The area of this parking lot is:
A=bs, using b found above you get:
A=(m-2s)s
A=ms-2s^2
dA/ds=m-4s and d2A/ds2=-4
Since acceleration is a constant negative, when the velocity equals zero, it is at the point where A(s) is the absolute maximum.
dA/dx=0 only when m=4s, so s=m/4
We are told that m=500, so s=125
A=ms-2s^2 Â so the maximum area is:
A(125)=500(125)-2(125^2)
A(125)=31250 ft^2
