The Big-M method is an adaptation of the Simplex Algorithm which is used as an alternative to the Two-Phase Simplex method. The pseudo-code for the Big-M method is as follows: ALGORITHM Big-M Input: An LP in canonical form with objective max z = f(x) and artificial variables y1, ..., Yp Output: An optimal solution to the LP or a statement that the LP is infeasible or unbounded 1: Let M be a very large constant 2: Modify the objective of the LP to maxz' = f(x) MX=1 Yi 3: Employ the standard Simplex Algorithm to solve the LP with the modified objective. The Optimality Criterion is satisfied when there are no more negative reduced costs in the columns of the non-artificial variables (a) Express the following LP in canonical form and solve using the Big-M method (b) Sketch the feasible region and identify the point associated to each tableau you obtained in (a). Hints: Use the symbol M in the Simplex tableau and NOT simply a large number of your choice. Note that you may choose not to add artificial variables to all constraints as in the algorithm. All you need to start the method is an initial Identity matrix in your coefficient matrix A. min z=-X1 12 s.t. X1 + x2 > 1 2x1 + 3x2 0