Robbie C. answered • 09/18/18
Tutor
New to Wyzant
Mathematics Grad Student - I want to help you succeed in math!
I'm assuming this is for calculus because it is a classic optimization problem. If it's not, let me know and I can try to explain it algebraically.
The first thing I do with problems like this is draw a picture. It helps me not to miss details. We know that the page has 60 square inches of print. We can represent the print by a rectangle with sides of lengths x and y, where x is the width and y is the length. So, xy=60, which means y=60/x (that will be helpful later).
The next step is to try to calculate the total area of the page. This is where the picture comes in handy. We can draw another rectangle with appropriate margins around the first rectangle. We know that the left and right margins are each 1 inch, so the page's width is 1+x+1, or x+2. The top and bottom margins are each 1.5 inches, so the page's length is 1.5+y+1.5, or y+3. Then the area of the page is A=(x+2)(y+3)=xy+3x+2y+6. We already know xy=60 and y=60/x, so we can substitute these in to get A in terms of x: A=60+3x+2(60/x)+6=66+3x+120/x.
From here you take the derivative of A with respect to x, set the derivative equal to zero to find the critical points, use the first derivative test to determine which value of x gives the minimum of A, and then use that value of x to determine y. Then, x and y are the dimensions of the printed area, and x+2 and y+3 are the dimensions of the page. I will leave this part of the process to you.
I hope this helps!
