Using Manipulate to Plot a Piecewise Function

Question

I want to plot a piecewise function with two variables using Manipulate command, but I am having trouble with it.

The function I want to plot is profit1. (details of the code can be found below)

z1 = Piecewise[{{Min[x1, 1 - p1], p1 < p2}, {Min[x1, Max[(1 - p1)/2, 1 - p1 - x2]], p1 == p2}, {Min[x1, Max[0, 1 - p1 - x2]], p1 > p2}}];
z2 = Piecewise[{{Min[x2, 1 - p2], p2 < p1}, {Min[x2, Max[(1 - p2)/2, 1 - p2 - x1]], p2 == p1}, {Min[x2, Max[0, 1 - p2 - x1]], p2 > p1}}];
profit1 = (p1 - c)*z1;
profit2 = FullSimplify[Integrate[1 - z, {z, 0, z1 + z2}] - c (z1 + z2)];

Values of x1, x2, and c are known and as follows: x1 = 1; x2 = 0.4; c = 0

So profit1 becomes:

When I try to use Manipulate to plot profit one:

Manipulate[Plot[profit1, {p1, 0, 1}], {p2, 0, 1}]

I get an empty graph like the one above. Any recommendations on how to fix this problem?

Thank you very much in advance.

Answer 1

profit1[p1_, p2_] := Which[
   p1 < p2, Min[1, 1 - p1], 
   p1 == p2, Min[1, Max[.6 - p1, (1 - p1)/2]], 
   p1 > p2, Min[1, Max[0, .6 - p1]],  
   True,  0];

Manipulate[
 Plot[profit1[p1, p2], {p1, 0, 1}],
 {p2, 0, 1}]

Incidentally, you might find this figure helpful:

Plot3D[profit1[p1, p2], {p1, 0, 1}, {p2, 0, 1},
       PlotPoints -> 50]