I work in a unit square. I have some conditions under which areas within the unit square are defined. Say for simplicity that there are two conditions which define two areas. For example, if y > 1/2 or if y > ax + b , we are in area 1 and otherwise, in area 2. I have represented two possible situations in the figures (Case 1 Case 2)
I want to find a and b (which are strictly positive) such that a*(area 1) + b*(area 2) is maximized. I think this is an easy problem to solve by hand, except if you have 7 different conditions. I am wondering if there is a way to automate that in Mathematica. The problem I have is that as conditions change, the shapes of the areas also change, which makes it difficult to compute them automatically (see the figures).
I would already be very happy if I could find all possible shapes given my seven conditions.
Anyone has an idea ?