Question

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

• A. At least two of the corner points
• B. All the corner points
• C. At least one of the corner points
• D. None of the corner points

Answer 1

Answer: (C)

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.