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Homework Help: Maximizing area

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A rectangle has sides on the x and y axes and a corner on the plane x+3y=12. Find its maximum area.


    2. Relevant equations

    A=xy=(12-3y)y

    (A=12, according to the solution manual.)

    3. The attempt at a solution

    At first I thought the corner it was talking about lay on one of the axes, but now I realize that it is a point around (4,3). I know there is a derivative (partial?) I need to take, but I don't know which one and or what to do it with respect to. I've drawn a graph so I can see what I'm doing, but the professor just skimmed over maximixation and I'm really confused! This chapter is not at a point that Lagrange multipliers have been covered. That's the way I would expect to do it, obviously not.
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Ok, if you want to maximize set dA/dy=0. What's y?
     
  4. Oct 16, 2008 #3
    dA/dy=12-6y. y=2, and then (12-3(2))*2=12 and that's the area. I knew it couldn't be that hard. thanks!
     
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