Question 1: Graphical method and sensitivity analysis (25 marks) Consider the following mathematical model: Max Z = 5x + y subject to 4x + 5y = 20 x-2y 2-2 Xy 20,x220 a. Find the optimal solution using graphical method. (15 marks) b. Report the screenshot of the sensitivity report of this model in Excel. (4 marks) c. Does the optimal solution change if we change the objective function coefficient of "y" to 6? Why? (You should answer this question based on the sensitivity report obtained in part (b) and without solving the model with new objective coefficient for y) (3 marks) d. Can we determine the optimal objective function value when we change the RHS of "Constraint 1" and "Constraint 2" to 30 and -5 respectively? Why? If yes, what is the optimal objective function value after this change? (You should answer this question based on the sensitivity report obtained in part (b) and without solving the model with new RHS values.)