A page is to contain 30 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.
2007-12-13 05:27:21 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let a and b be the sides.
Your constraint is that (a-2)(b-2) = 30
You seek to minimize ab.
Hmm. That looks a bit ugly. Let's let L = a-2 and W = b-2.
We seek to minimize (L+2)(W+2).
W = 30/L from the constraint. Substitute that back in, and you're minimizing c(L) = (L+2)(30/L + 2) = 2L + 34 + 60/L
Set the derivative equal to 0 and you're on your way!
(Note: This is one case where you don't have to worry about endpoints of the interval of possible values. It HAS no endpoints. The minimum, if one exists, WILL occur at a critical point.)
2007-12-13 08:16:03 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋