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Math Help - Function problem

  1. #1
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    Function problem

    A company produces very unusual CD's for which the variable cost is $8 per CD and the fixed costs are $50000. They will sell the CD's for $83 each. Let x be the number of CD's produced.
    Write the total cost as a function of the number of CD's produced.
    $

    Write the total revenue as a function of the number of CD's produced.
    $

    Write the total profit as a function of the number of CD's produced.
    $\

    An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length from the corners and folding up the sides.
    Write the volume Vof the box as a function of X. Leave it as a product of factors; you do not have to multiply out the factors.

    V=
    If we write the domain of the box as an open interval in the form (a,b) , then what is ?
    a=
    and what is ?
    b=
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  2. #2
    Senior Member topher0805's Avatar
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    I'm not sure I quite understand, but I'll give it a shot.

    Let's call the cost c, and the number of cd's produced n.

    We then have that:

    c(n) = 50,000 + 8n

    Let's call the revenue r. We then have that:

    r(n) = 83n

    Let's call the profit p. Profit can be defined as revenue minus cost, so we have:

    p(n) = 83n - (50,000 + 8n)

    Simplify it to get:

    p(n) = 75n - 50,000
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  3. #3
    Senior Member topher0805's Avatar
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    Sorry, didn't see the second part of your question!

    I assume that x is the length of the one of the sides of the squares that is being cut from the corners? If that is the case:

    Volume is equal to L*W*H. In this case the L and W will be the same, so we can say that:

    V = L^2*H

    And we know that the length L will be 16 - x, so we then have:

    V = (16-x)^2*H

    We also know that the height H will be equal to x, so we have that:

    V(x) = x(16-x)^2
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  4. #4
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    Quote Originally Posted by topher0805 View Post
    Sorry, didn't see the second part of your question!

    I assume that x is the length of the one of the sides of the squares that is being cut from the corners? If that is the case:

    Volume is equal to L*W*H. In this case the L and W will be the same, so we can say that:

    V = L^2*H

    And we know that the length L will be 16 - x, so we then have:

    V = (16-x)^2*H

    We also know that the height H will be equal to x, so we have that:

    V(x) = x(16-x)^2
    I plugged in the last part into webwork and it says that it is incorrect
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  5. #5
    Senior Member topher0805's Avatar
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    Is x supposed to represent the length of a side of the square cut from the corner?
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  6. #6
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    Quote Originally Posted by topher0805 View Post
    Is x supposed to represent the length of a side of the square cut from the corner?
    i am not sure, i wrote out the problem exactly as it shows in my assignment, and theres no picture to go along with it either
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  7. #7
    Senior Member topher0805's Avatar
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    Perhaps you could post a screen shot?
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    Quote Originally Posted by topher0805 View Post
    Perhaps you could post a screen shot?
    i dont know how to do that and i wrote out the problem exactly as it is though
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  9. #9
    Senior Member topher0805's Avatar
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    Hmm, then I must have made a mistake. I can't seem to find it though. Anyone else see any mistakes?
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  10. #10
    Super Member angel.white's Avatar
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    Quote Originally Posted by Girlaaaaaaaa View Post
    i dont know how to do that and i wrote out the problem exactly as it is though
    Try writing the area A of the box in terms of \alpha.
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  11. #11
    Super Member angel.white's Avatar
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    Anyway, if that made no sense, then you understand our dilemma. x is not defined, we don't know what it is, it could be the length of the side of one of the squares, or the total area removed from the 16x16 square, or the total area left after the pieces are removed, or the length of one of the sides after the pieces are removed, or any of an infinite number of other things.

    So in the same way that what I asked you to do made no sense, the question also makes no sense. You either need to figure out what they are asking you to do, or upload a screenshot.
    Quote Originally Posted by Girlaaaaaaaa View Post
    i dont know how to do that and i wrote out the problem exactly as it is though
    To take a screenshot, go look at the problem, then press the button on your keyboard labeled "print screen" (usually somewhere in the upper right of the keybaord).

    Then open any graphic software, windows comes with a default program called Paint which is usually located in startbar -> all programs -> accessories -> paint

    Open this, then press "ctrl+v" or go to edit -> paste

    A picture of your screen when you were looking at the problem should get pasted into the program.

    Go to file -> save as

    Give it a name like "I hate math" and under "save as type" select JPEG. And save it in your "my documents" folder.

    Then come back to this site, make a new post, type ten characters into the post, and scroll down to "additional options" there is a button labeled "manage attachments" click this button.

    A popup will appear, there will be a button labeled "browse" click this, navigate to the "my documents" folder, and select "I hate math.jpg" then click the button labeled "open" in the bottom right.

    You will be taken back to the popup. Directly to the right of the "browse" button will be a button labeled "upload" click this button. It will upload the file which may take a moment. Then in the upper right of the popup is the text "close this window" click that text. You will be taken back to your post, where you will see "I hate math.jpg" listed under "attach files" in the "additional options" section underneath of your post. This means it is uploaded. Then click "submit reply" and your screenshot will be posted to the site.
    Attached Thumbnails Attached Thumbnails Function problem-1-over-x-squared.png  
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  12. #12
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    Quote Originally Posted by Girlaaaaaaaa View Post
    [snip]
    An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length from the corners and folding up the sides.
    Write the volume Vof the box as a function of X. Leave it as a product of factors; you do not have to multiply out the factors.

    V=
    If we write the domain of the box as an open interval in the form (a,b) , then what is ?
    a=
    and what is ?
    b=
    The volume of the box is V = x(16 - 2x)^2.

    The 2 is there because the square are cut from all corners, so each side of the 16^2 material has x + x = 2x removed from it.
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  13. #13
    Senior Member topher0805's Avatar
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    Man, thank you so much! I've been going crazy trying to figure what I did wrong there!
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  14. #14
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    Quote Originally Posted by topher0805 View Post
    Man, thank you so much! I've been going crazy trying to figure what I did wrong there!
    It just needed a fresh pair of eyes, ol' bean
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  15. #15
    Super Member angel.white's Avatar
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    Don't congrate yourselves too soon, x can still be anything.

    But, on the bright side, Lynard Skynard just came on my playlist, so things are looking up at least.
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