Postal Regulations

Discussion in 'Algebra' started by nycmathguy, Jul 3, 2021.

  1. nycmathguy

    nycmathguy

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    See attachment. I am skipping part (b).

    Part (a)

    Volume = length • width • height

    V = y • x • x

    V = x^2 y

    V(x) = x^2 y

    I'm not sure about the domain.

    Part (c)

    The perimeter of the cross section is
    P = x + x + x + x + y.

    In short, P = 4x + y.

    Let P = 108 and solve for y.

    108 = 4x + y

    108 - 4x = y

    Plug 108 - 4x into V(x) for x.

    V(x) = x^2 (108 - 4x)

    V(x) = 108x^2 - 4x^3

    Factor

    V(x) = 4x^2(27 - x)

    Let V(x) = 0

    0 = 4x^2(27 - x)

    Set each factor to 0 and solve for x, where x represent the dimension that will maximize the volume.

    It is clear that 4x^2 = 0 leads to 0.
    So, x = 0 cannot be the answer.

    I know 27 - x = 0 leads to 27.

    I am going to say x = 27 is the only dimension
    for this application that will maximize the volume.

    You say?

    20210702_031700.jpg
     
    nycmathguy, Jul 3, 2021
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  2. nycmathguy

    MathLover1

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    see attached
     

    Attached Files:

    MathLover1, Jul 3, 2021
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  3. nycmathguy

    nycmathguy

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    I thank you. Can the maximum be found without calculus? This question is from a precalculus textbook.
     
    nycmathguy, Jul 3, 2021
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  4. nycmathguy

    MathLover1

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    maximum and minimum (or critical points) are points where the function is defined and its derivative is zero or undefined

    so, you have to use derivative to find max

    or you can find it from the graph (see attached)
    when you use

    https://www.symbolab.com/solver/step-by-step/V=108x^{2}-4x^{3}

    scroll down to see graph, you will see a point where max is, put mouse on it and the coordinates (18,11664) will pop out
     

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    Last edited: Jul 3, 2021
    MathLover1, Jul 3, 2021
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  5. nycmathguy

    nycmathguy

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    How is my effort?
     
    nycmathguy, Jul 3, 2021
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