CBSE Past Year MCQ Quiz

Assertion (A) : Consider a Linear Programming Problem with minimise \(\mathrm{Z}=\mathrm{x}+2 \mathrm{y}\) subject to constraints \(2 \mathrm{x}+\mathrm{y} \geq 3, \mathrm{x}+2 \mathrm{y} \geq 6\), \(\mathrm{x}, \mathrm{y} \geq 0\) which gives minimum Z at infinitely many points. The corner points of feasible region are \((0,3)\) and \((6,0)\).

Reason (R) : If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

The region represented by the system of inequations \(3 \mathrm{x}+\mathrm{y} \geq 3\), \(2 \mathrm{x}-\mathrm{y} \geq-5, \mathrm{x}, \mathrm{y} \geq 0\) is :