A certain magical substance that is used to make solid magical spheres costs $600 per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $70 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? T= ft. Note 1: the formulas for the volume and surface area of a sphere of radius r are V = 4³ and A=47² 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.
A certain magical substance that is used to make solid magical spheres costs $600 per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $70 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? T= ft. Note 1: the formulas for the volume and surface area of a sphere of radius r are V = 4³ and A=47² 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
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Transcribed Image Text:A certain magical substance that is used to make solid magical spheres costs $600 per cubic foot. The power of a magical sphere depends on its
surface area, and a magical sphere can be sold for $70 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.
r =
4² respectively.
=
=
Note 1: the formulas for the volume and surface area of a sphere of radius r are V 4³ and A
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.
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