Consider the following linear programming problem: Max Z = 10X + 5Y Subject to: X + 2Y = 18 Constraint Line (1) -4X + 3Y > -12 Constraint Line (2) 4X - Y > 0 Constraint Line (3) X,Y 20 a) Graph the constraint lines and mark them clearly with the numbers (1), (2), and (3) to indicate which lines correspond to which constraints. Shade in the feasible solution region and graph the objective function using a dotted line. Be sure to show your work. (8 marks) b) Solve the linear programming problem graphically and report the solution in a managerial statement. Provide all necessary calculations to justify your answer. (8 marks) Treat the following four questions independently (i.e., refer back to the original formulation for each question) c) In the problem that you graphed, there is a single optimal solution when it is maximized. Explain what would happen if it was a minimization problem. (1 mark) d) List the binding constraint(s). (1 mark) e) In the problem that you graphed, what would the coefficient of X in the objective function have to change to in order for there to be multiple optimal solutions? Show or explain how you were able to calculate this value. (2 marks) f) Solve this problem in Excel to verify your answer. Provide the Excel layout and answer report