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Question on optimization and limits

  1. Nov 21, 2009 #1
    You are designing a rectangular poster to contain 50 cm2 of printing with margins of
    4 cm each at the top and bottom and 2 cm at each side. What overall dimensions will
    minimize the amount of paper used?

    What i did was let the length and breath of the whole poster to be x and y so the area would be 50=(x-4)*(y-8) and perimeter=2(x-4)+2(y-8). Equate the area into the perimeter and differentiate Perimeter wrt y. However i got x=y which means its the maximum area?

    Limit as x tends to 0 [tex]\frac{e^x + e^-^x -2}{1-cos2x}[/tex]
    Applied Hopital rule once and got 0/2 however answer is 1/2. Am i correct?
     
  2. jcsd
  3. Nov 21, 2009 #2

    Mark44

    Staff: Mentor

    What does it mean to "equate the area into the perimeter"?

    I would approach this in a different way by letting w and h represent the width and height, respectively of the printed area. From these definitiions you get wh = 50.

    Now what you want to do is to minimize the area (not perimeter) of the overall piece of poster paper, so you want to minimize A = (w + 4)(h + 8). Use the other relationship to rewrite A as a function of only one variable, and then do your calculus magic.

    The stuff below seems to be unrelated to this problem.
     
  4. Nov 21, 2009 #3
    for the 2nd problm... apply it once again...it will give the correct answer
    after applyin it once it still gives 0/0 form...
     
  5. Nov 21, 2009 #4
    Got it guys thanks
     
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