Big M method in LPP

Question

In big M method the artificial variable is given cost as -M in case of maximisation problem. But what is the reason for taking "-M" ( M being a very large value)

Answer 1

Artificial variables are a trick used to get started with the simplex algorithm when, for example, you cannot find an easy initial feasible solution.

So you introduce the artifical variables, but you need to make sure that in the last iteration, they are not part of the basis. Giving them a $-M$ cost strongly penalizes them, and ensures that they will have negative reduced costs (if maximization), and therefore will not be part of the basis when optimality is reached.