3. [25 points] You are given the following linear programming model in algebraic form, with X1 and X2 as the decision variables: Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts). Minimize 40X1+50X2 Subject to 2X1+3X2>=30 2 X1+ X2>=20 X1>=0, X2>=0 a) Graph the feasible region and label the corner point. Compute the optimal solution using any method of your choice. Justify your answer and indicate the optimal solution on your graph. [10 points] b) How does the optimal solution change if the objective function is changed to 40 X1+70 X2? (10 points] c) Now your boss tells you "I apologize, but I was just informed that the X2 coefficient is not reliable, Can you tell me how much the X2 coefficient may change, both up and down, whereby the optimal solution you reported in problem 1(a) remains optimal?" Justify your answer. [5 points] 3. [25 points] You are given the following linear programming model in algebraic form, with X1 and X2 as the decision variables: Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts). Minimize 40X1+50X2 Subject to 2X1+3X2>=30 2 X1+ X2>=20 X1>=0, X2>=0 a) Graph the feasible region and label the corner point. Compute the optimal solution using any method of your choice. Justify your answer and indicate the optimal solution on your graph. [10 points] b) How does the optimal solution change if the objective function is changed to 40 X1+70 X2? (10 points] c) Now your boss tells you "I apologize, but I was just informed that the X2 coefficient is not reliable, Can you tell me how much the X2 coefficient may change, both up and down, whereby the optimal solution you reported in problem 1(a) remains optimal?" Justify your answer. [5 points]