Ask Question
30 December, 17:37

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 $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?

+5
Answers (1)
  1. 30 December, 17:46
    0
    x = 0.1428 ft

    Step-by-step explanation:

    Let x be radius of sphere

    Cost of magical sphere is

    700 $ per ft³ and the volume of the sphere of radius x is V = (4/3) * π*x³

    700 * (4/3) * π*x³

    The selling price is:

    Area of the sphere : 4*π*x² selling price = 50*4*π*x²

    Then my profit = selling price - cost

    P (x) = 200πx² - 700 (4/3) πx³

    Taking derivative both sides

    P' (x) = 400πx - 2800πx²

    P' (x) = 0 ⇒ 400πx - 2800πx² = 0

    xπ (400 - 2800x) = 0 x (400 - 2800x) = 0

    x = 0

    And 400 - 2800x = 0 x = 400/2800 x = 0.1428 ft
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers