Problem 1. (30 points) Consider the following LP model. Max Z= 3x1 - x2 + 2x3 subject to X1 + 0.5x2 + x3 4 x1 + x2 = 2 X1, X2, X3 20 a) (5 points) Change it to standard form. b) (20 points) Obtain all the basic solutions and indicate which ones are basic feasible solutions and write down the corresponding corner points. For each basic solution, you have to obtain the values of ALL the variables. c) (5 points) Obtain the solution of the LP problem, that is, obtain the values of the decision variables corresponding to the optimal solution as well as the optimal value of the objective function. Problem 1. (30 points) Consider the following LP model. Max Z= 3x1 - x2 + 2x3 subject to X1 + 0.5x2 + x3 4 x1 + x2 = 2 X1, X2, X3 20 a) (5 points) Change it to standard form. b) (20 points) Obtain all the basic solutions and indicate which ones are basic feasible solutions and write down the corresponding corner points. For each basic solution, you have to obtain the values of ALL the variables. c) (5 points) Obtain the solution of the LP problem, that is, obtain the values of the decision variables corresponding to the optimal solution as well as the optimal value of the objective function