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  1. #1
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    Word problem involving rectangle area...

    A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

    I can handle the differentiation part. Just need the equation
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  2. #2
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    Quote Originally Posted by struck View Post
    A rectangular sheet of metal measures 50cm by 40cm. Equal squares of side x cm are cut from each corner and discarded. The sheet is then folded up to make a tray of depth x cm. What is the domain of possible values of x? Find the value of x which maximizes the capacity of the tray.

    I can handle the differentiation part. Just need the equation
    1. You can't cut off more than 20\ cm\times20\ cm-squares because then the width of the sheet would be zero. Therefore

    D=\{x|0\leq x \leq 20\}

    2. the volume of a prism is calculated by:

    V = (base\ area) \cdot height

    The base area is a rectangle which measures (50-2x)(40-2x)

    3. Therefore the function of the volume wrt x:

    V(x)=(50-2x)(40-2x)\cdot x

    4. Go ahead!
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