(1 point) A certain magical substance that is used to make solid magical spheres costs $700...

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(1 point) A certain magical substance that is used to make solid magical spheres costs $700 per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $40 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? ft. Note 1: the formulas for the volume and surface area of a sphere of radius r are V = and A = 4ar2 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. (1 point) A certain magical substance that is used to make solid magical spheres costs $700 per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $40 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? ft. Note 1: the formulas for the volume and surface area of a sphere of radius r are V = and A = 4ar2 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.