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Definition: Infeasibility - Degeneracy
Infeasibility in a linear program occurs when there exists no solution which is able to satisfy all the stated constraints of the given problem. Taking into account that in reality all models must have a solution, when an infeasibility occurs usually two conclusions are drawn. The first being that there is error in defining the constraints of the problem or some numbers have been written down wrong. Infeasibility given an indication of some mismatch between the demand and the supply. Often adding a slack variable in modelling prevents infeasibility.
If a LP has an objective function as Min X1+ X2, and its constraints are X1<=7, X2<=7 and X1+ X2 <=13 then this modelling will be infeasible. However by adding slack variable to the objective the infeasibility can be removed.
Degeneracy occurs when one of the basic variable of the feasible solution takes a zero value. It usually occurs due to redundant constraints and increases the number of iterations that take place in LP modelling.