minimum area problem

S

sjones11

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Jul 15, 2005
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I'm trying to help a friend of mine with a pre-calc problem. Here it is:

You have a sheet of paper with a printable region of 48 sq. in.

The margins on top and bottom are 1 in.

The margins to the left and right are 1.5 in.

What is the length & width of the sheet of paper with the SMALLEST total area?

Code: 
 ---------------------------
|              ^  <--1       |
|              v             |
|        ------------        |
|       |            |       |
|       |   A=48     |       |
|       |            | <1.5> |
|       |            |       |
|        ------------        |
|                            |
|                            |
 ---------------------------

Sorry for the bad drawing but hopefully it helps :)

Thanks in advance!
 
Using your drawing:

Label the horizontal component of your printable image, H.
Label the vertical component, V.

We have H*V = 48 ==> V = 48/H
Area of entire page, then, is (H+3)*(V+2) = (H+3)*((48/H)+2).

If f(H) = (H+3)*((48/H)+2), with a Domain of (0,48), there aren't too many places to look to find a minimum value, but since you did not post in the calculus section, I'm not sure what to tell you. You can draw a nice picture and see that the minimum total page area occurs at a little greater than H = 5.

Maybe I just need a nap and I'm not seeing straight?

So, where does that leave us. Guess and check?
 
Repaired above.

When you type it three times, it is not longer just a typo. It is simply an error.

See, I told you I needed a nap.
 
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