Sketching Graphs of P(a,b) in Planar Plane: 2D Solution

[-EquinoX-]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[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.

 

[Mark44]

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.

 

[-EquinoX-]

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

 

[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.

 

[-EquinoX-]

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.

gotcha! thanks everyone