A book designer has decided that the pages of a book should have 1-in. margins a

Question

A book designer has decided that the pages of a book should have 1-in. margins at the top and bottom and 1/2-in. margins on the sides. She further stipulated that each page should have an area of 32 in.2 (see the figure below). Determine the page dimensions that will result in the maximum printed area on the page.

x = in y = in A book designer has decided that the pages of a book should have 1-in. margins at the top and bottom and 1/2-in. margins on the sides. She further stipulated that each page should have an area of 32 in.2 (see the figure below). Determine the page dimensions that will result in the maximum printed area on the page.

Explanation / Answer

area x*y=32 ==>y=32/x

printed are A=32-(1/2*Y+ 1/2*Y +1*X+ 1*X)

=32-(y+2x)

=32-(32/x +2x)

=(32x -32 -2x^2)/x

dA/dx=0

==>((32-4x)*x -(32x -32 -2x^2))/x^2=0

==>2x^2= 32

==>x=4inch

==>y=8inch

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