# Sketching a graph

1. Feb 3, 2009

### -EquinoX-

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

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

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. Feb 3, 2009

### CompuChip

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.

3. Feb 3, 2009

### 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.

4. Feb 3, 2009

### -EquinoX-

ok then, at first place I thought this problem asks me to draw a contour diagram...

5. Feb 3, 2009

### CompuChip

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.

6. Feb 3, 2009

### -EquinoX-

gotcha! thanks everyone