Question

maxima and minima....

A rectangular page is to contain 24 in^2 of print. The margins at the top and bottom of the page are each 1 1/2 in. wide. the margins on each side are 1 in. What should the dimensions of the page be so that the least amount of paper is used?

Answer 1

hmm.. I would like to help you but i'm not used to work with inches. In my coutry we use the metric system

Answer 2

need an answer for my recitation ahhhhhhh!!!

Answer 3

we can do this if you like. not that bad

Answer 4

if you put x = width of paper and y = height, you know that the area is
\[A=xy\] and also that
\[(x-2)(y-3)=24\]
\[\frac{24}{x-2}+3=y\]
\[y=\frac{3x+18}{x-2}\]
\[A(x)=x(\frac{3x+18}{x-2})=\frac{3x^2+18x}{x-2}\]
\[A'(x)=\frac{3(x^2-4x-12)}{(x-2)^2}\] critical point where
\[x^2-4x-12=0\]
\[(x-6)(x+2)=0\]
\[x=6\] is your answer because the negative one makes no sense here.