December 3rd, 2015, 04:03 AM  #1 
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  Help to find the dimensions
Hello All: I have this Question. I really don't know how to answer it. Can someone help me and thanks for all. The Question is: Poster is to be designed with 50 in2(Square) of printed type, 4 inch margins on both the top and the bottom, and 2 inch margins on each side. Find the dimensions of the poster which minimize the amount of paper used. Last edited by skipjack; December 3rd, 2015 at 05:22 AM. 
December 3rd, 2015, 04:20 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
For a printed area $x$ wide by $y$ high, we require a printed area $xy = 50$. The paper width is $x+4$ (the printed width plus a border of 2 at each side). The paper height is $y+8$ (the printed height plus a border of 4 each at the top and bottom). The total area of paper used is then $f(x)=(x+4)(y+8) = xy + 8x + 4y + 32$, but we have $xy=50$ so $y = {50 \over x}$. Putting both of these into the equation gives $$f(x) = 50 + 8x + {200 \over x} + 32 = 82 + 8x + {200 \over x}$$ The minimum value of this function specifies the printed width we require. From that, you can work out the paper size. Last edited by skipjack; December 3rd, 2015 at 05:11 AM. 
December 3rd, 2015, 04:32 AM  #3  
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  Quote:
Last edited by skipjack; December 3rd, 2015 at 05:13 AM.  
December 3rd, 2015, 05:19 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,020 Thanks: 2255 
Is it readable now? The minimum (for $x$ > 0) occurs for x = 5.

December 3rd, 2015, 06:37 AM  #5 
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  
December 3rd, 2015, 06:47 AM  #6  
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  Quote:
Last edited by skipjack; December 3rd, 2015 at 09:29 AM.  
December 3rd, 2015, 08:25 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
Yes, you can solve for $x$. Once you have $x$, you can calculate $y$ and anything else you want.

December 4th, 2015, 07:33 AM  #8 
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  Does in finally x = 2 ?? or = 2 ?
Last edited by ahmed2009; December 4th, 2015 at 07:37 AM. 
December 4th, 2015, 07:53 AM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra  Skipjack got $x=5$. That's probably correct.

December 5th, 2015, 01:25 AM  #10 
Member Joined: Nov 2015 From: saudi arabia Posts: 30 Thanks: 5  

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