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Math Help - NEED HELP FAST! Derivitives/cost application

  1. #1
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    NEED HELP FAST! Derivitives/cost application

    ok so i have this problem and i think ive got it figured just need a little help

    we have a box with a square base and a volume of 4000cm^3

    the sides and top cost 4.5$/m^2
    the cost of the bottom is 7$/m^2

    I am supposed to see how much it wil cost for minimum cost to make the box so...
    Let x represent the length and width (since square base) let "y" rep height
    V= 4000
    4000=x^2y

    y=4000/x^2

    Than use surface area formula (including cost function?)
    SA= 7(x^2) + 4.50(x^2) + 4.50 (4xy)
    =11.50x^2 +18x(4000/x^2) (subbed Y value in from volume equation)
    =11.50x^2 + 72000/x

    than take derivitive
    23x -72000/x^2

    set to zero

    23x^3 = 72000
    x=14.6286?...

    one more problem i have in the end..now how do i solve the problem of the cm^2 and the M^2 should i just divide the 4000 by 10000( or 1000 im not sure?) immediately or how should i deal with that?
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by jamman790 View Post
    ok so i have this problem and i think ive got it figured just need a little help

    we have a box with a square base and a volume of 4000cm^3

    the sides and top cost 4.5$/m^2
    the cost of the bottom is 7$/m^2

    I am supposed to see how much it wil cost for minimum cost to make the box so...
    Let x represent the length and width (since square base) let "y" rep height
    V= 4000
    4000=x^2y

    y=4000/x^2

    Than use surface area formula (including cost function?)
    SA= 7(x^2) + 4.50(x^2) + 4.50 (4xy)
    =11.50x^2 +18x(4000/x^2) (subbed Y value in from volume equation)
    =11.50x^2 + 72000/x

    than take derivitive
    23x -72000/x^2

    set to zero

    23x^3 = 72000
    x=14.6286?...

    one more problem i have in the end..now how do i solve the problem of the cm^2 and the M^2 should i just divide the 4000 by 10000( or 1000 im not sure?) immediately or how should i deal with that?
    I would convert the units to m^3 at the very beginning. 4000 cm^3 into m^3

    There are 100 * 100 * 100 = 1 000 000 cm^3 in a m^3. The work looks ok, except for the units.

    Good luck!!
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