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Q. The objective function of $LPP$ defined over the convex set attains its optimum value at

MHT CETMHT CET 2017Linear Programming

Solution:

Let $Z = ax +$ by be the objective function
When $Z$ has optimum value(maximum or minimum), where the variables
$x$ and $y$ are subject to constraints described by linear inequalities,
this optimum value must occur at a corner points of the feasible region.
Thus, the function attains its optimum value at one of the corner points.