Hi yorkey,

I did this with a TI-84+ and shaded the "wanted region" which we call the "feasible region" in linear programming.

The intersections of the three lines are at (4, 4), (4, 8) and (6, 6).

Your "profit" function would be P(x, y) = 3x + 1.5y

Substitute the points of intersection into this function to determine the greatest and least values.