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Sketching a graph

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Say I have a function:

    P(a,b) = 2500a + 11000b - 6000

    Question asks for:
    Sketch curves of constant profit in the ab-plane for P = 10000, P = 20000, and P = 30000 and the break-even curve P = 0. Describe your diagram below.

    My question is that will this be a graph of a 2-D in a planar plane or is it 3-D?
    How do you graph it?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 3, 2009 #2


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    Homework Helper

    Let's look at the first one, P = 10 000. If you plug that in, you get
    10 000 = 2 500 a + 11 000 b - 6 000

    There are two variables, so you can plot this in 2-D. For example, put a on the x-axis, b on the y-axis and draw the curve corresponding to the formula. The first time, I suggest that you explicitly re-write it to the formula for a straight line (e.g. b = ... a + ...). Once you see that it is indeed a straight line, you can just plug in two values for a, find the values for b - then draw the two points you found and draw a straight line through it.
  4. Feb 3, 2009 #3


    Staff: Mentor

    To graph P(a, b) = 2500a + 11000b - 6000 requires three dimensions, and the graph will be a plane.

    For each fixed value of P, though, the graph is a line that you can show in a two-axis system. Each of these lines would be a horizontal cross-section in the three-dimensional graph.
  5. Feb 3, 2009 #4
    ok then, at first place I thought this problem asks me to draw a contour diagram...
  6. Feb 3, 2009 #5


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    Yes, that is exactly what it is: a contour plot with just 4 level curves.
    So if you have treated that in class, it should also follow from the theory you learned that it can be done in 2D.
  7. Feb 3, 2009 #6
    gotcha! thanks everyone
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