A rectangular page is to contain 50 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide. Find the dimensions of the page that will minimize the amount of paper used. (Let x represent the width of the page and let y represent the height.)

Question

anonymous · Answer

Here's the problem, restated more concisely.
Let ab=50. Find a and b such that (a+2)(b+4) is the least. Do you follow me there?

anonymous · Answer

yeah

anonymous · Answer

Are you familiar with calculus?

anonymous · Answer

yes. i have that class right now and this is our hw problem

anonymous · Answer

OK. So let's say a is the width, b is the length. Now, you have the techniques to minimize a function in calculus: you set the derivative to 0. But first you need to put the problem in only 1 variable. So how can you state the problem in 1 variable only? Can you find a relationship between a and b given by the problem?

anonymous · Answer

|dw:1381897696083:dw|

anonymous · Answer

What's y and what's x?

anonymous · Answer

oh well i used y instead of h and x instead of b

anonymous · Answer

i mean i used y for length and x for width

anonymous · Answer

Alright. How did you get that?

anonymous · Answer

well i just first set up the problem as (x-2)(y-4)=50

anonymous · Answer

Right. So now what equation do you have to minimize?