Question 1113217: A printed page has 1-inch at the top and bottom, and 3/4-inch margins on each side. The area of the printed portion of the pages is 48 square inches. Find the dimension of the page, which has the smallest possible area.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x is width, y is length of printed area
xy=48
the whole page is x+1.5 inches and y+2 inches
xy+2x+1.5y+3 has to be minimized. xy=48
2x+1.5(48/x)+51 has to be minimized
2x+(72/x)+51
Take the derivative and set equal to 0.
2-(72/x^2)=0
72=2x^2
x^2=36
x=6 inches
y=8 inches
second derivative is +144/x^3, which is positive, so the critical point is a minimum.
The page has dimensions of 7.5 x 10 or 75 in^2,
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