minimize z = x1 s.t. 4x + 3x 12 2x1 x2 > 2 x1, x2 > 0 X2 (a) find the optimal solution to the above model using the graphical method (b) Suppose x3 and x4 are slack and surplus variables for the first and second constraints respectively. Consider the basic solution where x = (x1, x4) then set up the corresponding Simplex iteration and find the optimal solution using the Simplex Algorithm. (c) Suppose that the inequality in the second constraint is replaced by 2x1 X 2. Find the optimal solution using the tableau based Simplex Algorithm. (Caution: the objective is a "minimization"),