Part Three: (50%) We have the following linear programming model: MAX Z = 3x1 + 4X2 SUBJECT TO 2x1 + x 6 2x1 + 3x2 9 X1, X2 0 (P1) Draw a graph for this model and find its optimal solution (Indicate this optimal solution in the graph). (P2) Both variables in the model are required to be integers, what is the optimal solution now (Indicate this optimal solution in the graph)? (P3) Compare these two models and discuss them briefly (the number of feasible solutions, the optimal solutions are the same or not).

Part Three: (50%) We have the following linear programming model: MAXz=3x1+4x2 SUBJECT TO 2x1+x262x1+3x29x1,x20 (P1) Draw a graph for this model and find its optimal solution (Indicate this optimal solution in the graph). (P2) Both variables in the model are required to be integers, what is the optimal solution now (Indicate this optimal solution in the graph)? (P3) Compare these two models and discuss them briefly (the number of feasible solutions, the optimal solutions are the same or not)