Problem 1: Describe graphically what the simplex method does step by step to solve the following problem. Maximize Z = 2x1 + x2 Subjct to: X2 0 (20 Points) Problem 2: Reconsider the model in Problem 1. (a) Introduce slack variables in order to write the functional constraints in augmented form. (b) For each CPF solution, identify the corresponding BF solution by calculating the values of the slack variables. For each BF solution, use the values of the variables to identify the nonbasic variables and the basic variables. (c) For each BF solution, demonstrate (by plugging in the solution) that, after the nonbasic variables are set equal to zero, this BF solution also is the simultaneous solution of the system of equations obtained in part (a)