I was given the following linear programming problem and have been asked to find all optimal solutions graphically. I am quite new to the subject, so please forgive my naivety.
minimize: z = x - y subject to: x + y <= 6 x - y >= 0 y - x >= 3 x, y >= 0
I've graphed the constraints as shown below:
To me, it seems like there are no optimal solutions because there is no feasible region (that is, a region where all constraints are satisfied and therefore all three shaded colors would overlap). Is my assumption correct or is there an optimal solution(s) to this problem and how can I go about finding it(them) graphically?