Assertion (A): Consider a Linear Programming Problem with minimise Z = x +2 y subject to constraints 2 x + y ≥ 3, x +2 y ≥ 6, x, y ≥ 0 which gives…

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