business calculas

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A cylindrical can is to hold 20 pie mraised to the 3rd power. The material for the top and bottom costs $10/m raised to the 2nd power and material for the side costs $8/m to the 2nd power. Find the radius r and height h of the most economical can.

  • business calculus -

    Volume = pi r^2 h = 20 pi (m^3)
    Therefore r^2 h = 20
    h = 20/r^2

    Cost = 2 pi r^2 * 10 + 2 pi r h * 8
    = 20 pi r^2 + 16 pi r(20/r^2)
    = 20 pi r^2 + 320 pi/r

    Set the derivative with respect to r equal to zero.

    40 pi r = 320 pi r^-2
    r^3 = 80
    r = 4.31 m

    Check my math

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