Question 1: Graphical method and sensitivity analysis (25 marks) Consider the following mathematical model: MaXZ :5x+y subject to 4x+ 5y S 20 x72); 2 *2 26120,.762 20 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.) (3 marks) instruction: - Round all numbers to 2 decimal places. - To answer part (a), you should do the followings: '/ Draw each constraint boundary line by generating arbitrary goints! and report these points in your answer. Label each line on the graph. '/ Show each constraint on the graph by a line arrow on the corresponding constraint boundary line. It means that you should show which side of a constraint boundary line corresponds to the constraint. Show the feasible region. Find all corner points. You should show how you calculate each corner point. Show the objective function line on the graph. Show the direction of improving the objective function on the graph. \\\\\\\\\\ Show the optimal solution on the graph! and explain how you have found it