Consider this problem and answer the following questions. Maximize Z= 2x1 + 3x2 s.t. C1: x1 + 2x2 = 0 1. Solve the problem graphically in a free hand manner: identify all the CPFs, the optimal solution and optimal objective value 2. Use hand calculation to solve the problem by the simplex method in algebraic form 3. What can you say about the solution if the RHS of the second constraint (C2) was 16 (i. e. b2 = 16)? What is the new solution? Solve by simplex method in algebraic and show this case graphically (show the CPF visited on the graph in order, starting from initial feasible solution at origin). 4. What can you say about the solution if the RHS of the second constraint (C2) was 14 (i. e. b2 = 14)? What is the new solution? Solve by simplex method in algebraic form and show this case graphically (show the CPF visited on the graph in order, starting from initial feasible solution at origin). 5. What if the RHS of the first constraint (C1) was 25 (i. e. b1 = 25)? Does the solution change? if so, show how does it change? Solve by simplex method in algebraic form and show this case graphically (show the CPF visited on the graph in order, starting from initial feasible solution at origin) 6. What if the coefficient of x1 in the objective function was 4 (i. e. c1 = 4)? How does the solution change? Solve by simplex method in algebraic form and show this case graphically