How should we deal with strict inequalities in a linear programming problem? For example:
inequalities such as $ax< b$;
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In general strict inequalities are not treated in linear programming problems, since the solution is not guaranteed to exist on corner points.
Consider the $1$-variable LPP: $Max$ $x$ subject to $x<3$. Now there does not exist any value of $x$ for which maximum is achieved and which lies in the feasible region.