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 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 maxz0 = f(x)−mpp i=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
solve the following lp by using the big-m method
minz = 2x1 + 3x2 −5x3
s. t.
x1 + x2 + x3 = 7
2x1 −5x2 + x3 ≥ 10
x1,x2,x3 ≥ 0