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##### Linear Programming – Notes

**Linear Programming Problem**

Theorem2: If R is open, then a maximum or a minimum value of the object function may not exist. However, if the exists, then it must occur at a corner point of R.

Case (i): P is the maximum value of z, if the open half plane determined by ax +by > P has no point in common with the feasible region. Otherwise, Z has no maximum value.

Case (ii): Q is the maximum value of z, if the open half plane determined by ax +by > Q has no point in common with the feasible region. Otherwise, Z has no maximum value.