I am having trouble with a word problem. I know I have to set up the minimizing function then i can state the domain then find the minimum dimensions as well. I just confuse overall so please help.
7) A page is to contain 30 square inches of print. The margins at the top and the bottom of the page are each 2 inches wide. The margins on each side are only 1 inch wide. Find the dimesions of the page so that the least paper is used.
Suppose that the printed part is a rectangle of sides x and y (x will be the length, y the height). And assuming that the paper is rectangular..
The area of the printed part is
Since there is a margin on top and on bottom of 2 inches each, the height of the paper will be
And since there are two lateral margins of 1 inch each, the length of the paper will be
Hence the area of the paper will be
So find x and y such as A is minimized, and remember that
Hence I'd advise you to develop the expression for A