the images correspond to 2D math of

piecewise(0 < x and x < 4, 8, 4 <= x and x < 20, -.5*x+10);

and

piecewise(x < 4, y-8 = 0, 0 <= x and x < 20, y+.5*x-10 = 0);

respectively.

Thanks Markiyan.

One problematic example is one in which the budget set is not a function in all sections. For example a budget set that is broken in three sections: from x=0 to 4, the budget is defined as y=8. From x > 4 to x < 10 y = -0.5x + 10 and finaly x = 10 for y < 5.

Perhaps part of my problem is my inability to specify an implicit piecewise expression. Following the same example (and supposing the function where not a simple line, but a more complex function) and not withstanding the non-function segment, if the budget set where defined explicitly like 

I can plot it without any problem, but if it is defined implicilty like

plotting won't work. The problem goes beyond plotting since that could be done with line segments, what I would like to do is be able to work with more complex examples and operate on them as I would with any normal funciton.