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March 30, 2017

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Each page of a book will contain 30 in squared of print, and each page must have 2 inch margins at top and bottom and 1 inch margin at each side. What is the minimum possible area of such a page.

  • calculus - ,

    if the page width = w, the height = 30/w
    Allowing for two margins on each dimension,

    a(w) = (width + 2*2)(30/w + 2*1)
    = (w+4)(30/w+2)
    = 30 + 2w + 120/w + 8
    = 2w + 120/w + 38

    area is min where da/dw = 0

    da/dw = 2 - 120/w^2
    2w^2 = 120
    w^2 = 60
    w = 7.75

    a(7.75) = 68.98 -- call it 69 in2

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