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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