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Math Help - Problem with creating a formula

  1. #1
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    Problem with creating a formula

    Question:

    Attachment 20448

    a) We have a folded box shaped like a rectangle with the length b and width a. The box has four squares that we fold up, these squares are the height of the box x. Choose a couple of values for length b and width a and decide what x has to be in order for the box to have the largest volume.

    b) Produce a formula that enables you to calculate what x has to be in order to get the largest volume when only given the length a and width b.

    My attempt to a solution:

    a)

    1. First i got to make a function that describes the volume of the box
    2. Derive the function in order to find the maximum point of the function
    3. Find out which x-values that can't be a part of the solution (this is where my first problem lies) for example that x > 0 but can't be larger than...
    4. If both x values are a part of the solution, then find out which one lies at a maximum point and finding the y coordinate by inserting the x value into the normal function.

    Length: b-2x
    Width: a-2x
    Height: x

    Attempt 1:

    y= x(b-2x*a-2x)
    y= x(ab + b*-2x + a*-2x +4x^2)

    I then chose a = 20 b = 5 (measured in cm) this gave me

    y= x(20*5 +5*-2x -20*-2x +4x^2)
    y= 4x^3 -50x^2 +100x
    y= 12x^2 -100x +100
    y= x^2 - 25/3x + 25/3

    When solving the equation using the quadratic formula i get x= 1,16 and x= 7,16 and when searching for the maximum point i get that when x= 1,16 we're at a maximum point which gives us y = 54,94. The maximum volume being 54,94cm^3 when x = 1,16.

    Attempt 2:

    a= 10
    b=5

    On attempt 2 i got x = 3,94 and x= 1,05 and the maximum point was at x= 1,05 and y= 54,5

    Attempt 3:

    a= 40
    b= 20

    On attempt 3 i got x= 15,77 x= 4,22 and the maximum point was at x= 4,22 and y= 1539,59.

    b) This is where my problem lies, creating a formula where i only need a and b to get what x needs to be in order to get the maximum volume

    Thanks in advance Mathmen
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  2. #2
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    I apologize I just noticed that my attachment didn't go through. It was more or less just a picture of a folded box shaped as a rectangle with the length b and width a. At each corner there were small squares with the length x
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  3. #3
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    Are you allowed to use Calculus?
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  4. #4
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    I'm allowed to use any method as long as it works with the examples above
    Last edited by Mathmen; January 15th 2011 at 06:22 AM.
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  5. #5
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    I solved thanks anyways
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  6. #6
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    The underlying question

    Quote Originally Posted by Mathmen View Post
    I'm allowed to use any method as long as it works with the examples above
    I think the underlying question is whether you studied calculus yet?
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