Unboundedness in a linear programming problem can be identified during the Simplex Method when a basic variable's positive coefficient in the objective function row has no constraints limiting its increase, indicated by non-positive ratios of RHS values to the corresponding column coefficients. This situation suggests that the objective function can increase indefinitely without bounds.

Unboundedness in a linear programming problem can be identified through several methods. Using the Simplex method, if the algorithm continues to improve the objective function value indefinitely without finding an optimal solution, the problem is unbounded. Graphical analysis can also help; if the feasible region extends infinitely in the direction of optimization without constraints, it indicates unboundedness. Additionally, examining the constraints can reveal if there are missing limits on decision variables, allowing for infinite values in the objective function.