2. (a) convert the following lp to canonical form: min z = 2x1 + 3.12 – 5.23 s. t. xi + x2 + x3 = 7 2x1 – 5x2 + x3 > 10 21, x2, x3 > 0 (b) solve the above lp using the two-phase simplex method. 3. 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 maxz = f(x) and artificial variables yı, 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 max z' = f(x) – m p _, 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 solve the lp from q2 by using the big-m method (hint: use the symbol m in the simplex tableau and not simply a large number of your choice).