Posted by Barbara on Tuesday, November 1, 2011 at 1:13am.
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  Steve, Tuesday, November 1, 2011 at 11:22am
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 in^{2}
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