A rectangular page is to contain 30 quare inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margin

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A rectangular page is to contain 30 quare inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide. Find
the dimensions of the page such that the least amount of paper is used.

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  1. Answer:

    Step-by-step explanation:

    Print

    xy = 30

    x = 30/y

    f(y) = 2x + 2y = minimum

    f(y) = 2(30/y) + 2y = minimum

    f'(y) = 2 – 60/(y^2)

    0 = 2 – 60/(y^2)

    60/(y^2) = 2

    y^2 = 30

    y = √30

    √30 * x = 30

    x = √30

    print: √30 x √30

    2

    Paper

    you have to add 2 to the length and width because the paper margins are 1 on each side

    √30 + 2 x √30 + 2

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