A certain magical substance that is used to make solid magical spheres costs $\$500$ per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $\$50$ per square foot of surface area. If you are manufacturing such a sphere, what size should you make them to maximize your profit per sphere?
$r=$ ft.

Note 1: the formulas for the volume and surface area of a sphere of radius $r$ are $V=\frac{4\pi}{3}r^3$ and $A=4\pi r^2$ respectively.

Note 2: on a real exam you would be expected to justify that the answer above is actually a maximum, rather than, say a minimum.