Calculus problem help
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Calculus problem help
I've gotten most of the problems for this lab, but I can't seem to figure this one out. I know there are some math gurus on here, so please chime in. Thank you in advance.
A publisher wants the book they're doing a layout for to contain 28in^2 of printed matter per page and have side margins of 1 1/2 in and top/bottom margins of 1 1/4 in. What size page can accomplish this, while using as little paper as possible?
I know that you have to come up with two formulas, combine them, and find the derivative to come up with the answer, I just can't derive the two equations.
A publisher wants the book they're doing a layout for to contain 28in^2 of printed matter per page and have side margins of 1 1/2 in and top/bottom margins of 1 1/4 in. What size page can accomplish this, while using as little paper as possible?
I know that you have to come up with two formulas, combine them, and find the derivative to come up with the answer, I just can't derive the two equations.
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Let:
h = height of printed area
w = width of printed area
Then:
wh = 28
w = 28 / h
The area of the page is:
A = (w + 1.5 + 1.5) * (h + 1.25 + 1.25) = (w + 3) * (h + 2.5) = (28 / h + 3) * (h + 2.5)
Solve dA/dh = 0 for h, then compute w.
h = height of printed area
w = width of printed area
Then:
wh = 28
w = 28 / h
The area of the page is:
A = (w + 1.5 + 1.5) * (h + 1.25 + 1.25) = (w + 3) * (h + 2.5) = (28 / h + 3) * (h + 2.5)
Solve dA/dh = 0 for h, then compute w.
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From: Los Angeles
Originally Posted by magician,Mar 30 2007, 02:41 PM
Let:
h = height of printed area
w = width of printed area
Then:
wh = 28
w = 28 / h
The area of the page is:
A = (w + 1.5 + 1.5) * (h + 1.25 + 1.25) = (w + 3) * (h + 2.5) = (28 / h + 3) * (h + 2.5)
Solve dA/dh = 0 for h, then compute w.
h = height of printed area
w = width of printed area
Then:
wh = 28
w = 28 / h
The area of the page is:
A = (w + 1.5 + 1.5) * (h + 1.25 + 1.25) = (w + 3) * (h + 2.5) = (28 / h + 3) * (h + 2.5)
Solve dA/dh = 0 for h, then compute w.
Seriously, it's great that you help everyone out with any math problem.
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Joined: Jul 2001
Posts: 6,592
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From: Yorba Linda, CA
Originally Posted by npham,Mar 30 2007, 04:21 PM
I knew I could rely on your Magician. Thanks a lot. By the way, What university do you teach at?
I teach mathematics at Cal State, Fullerton and finance and risk management at UC, Irvine.
