The two-phase method requires us to solve two separate linear programs before obtaining an optimal..

The two-phase method requires us to
solve two separate linear programs before obtaining an optimal solution—one
problem to find a basic feasible solution, and the other to solve our original
problem to optimality. When an initial basic feasible solution is not apparent,
we can solve our problem using only one linear program by penalizing the
artificial variables by solving large negative number −M (M > 0) in
the objective function. For example, the linear program

canbe rewritten as

where M is a large positive number.
If M is large enough, then any infeasible solution will have negative objective
value, while every feasible solution will have nonnegative value. We can then
use the simplex method to solve this problem, keeping M as a parameter
throughout. This method is called the Big-M Method. Solve this problem using
the Big-M method.