Determine the page dimensions that will result in the maximum printed area on the page.

Question

A Publiser decided that the pages of a book should have a 1-in. margin at the top and the bottom, and a (1/2) -in. margin on each side of the page. He further stipulated that each page of the book should have an area of 50 in.2

Answer 1

Draw a figure.

Let W=width of the page and H=height of the page and P=printed area

WH=50

P=(W-1)(H-2)

Substitute from the first equation into the 2nd and the set the derivative of P equal to 0.

Solve for the variable (whichever you chose to keep).