Urgent..Please Help...Word Problem

[mathlover23]

Hello. I apologize for bothering you with such an easy problem but I am having difficulty with the following optimization problem:

A piece of paper contains 60 square inches of print. The margins at bottom of the page and the top of the page are 1.5 inches wide whereas the side margins are only 1 inch. What should the dimensions of print be so that a minimum amount of paper is utilized?

I drew a diagram and my primary and secondary equations were Perimeter and that of Area with the whole paper being P= 2w + 2l and the Area of the print being A= (x-2)(y-3). I think I am going about this wrong. please help me. Thanks so much!!!!

 

[stapel]

First, THANK YOU for showing your work!!

Second, let's see if we can reduce this to one variable.

. . . .printed area:
. . . .height: h
. . . .width: w
. . . .area: hw = 60

Then h = 60/w.

. . . .paper area:
. . . .height: h + 3
. . . .width: w + 2
. . . .area: (h + 3)(w + 2)

Substituting from the first part, we get:

. . . .(60/w + 3)(w + 2) = A(w) = 60 + 3w + 120/w + 6

Minimize.

Eliz.