The corner points of the feasible region determined by a set of linear constraints are : (0,0), (0, 4), (2, 5), (6, 3) and (6, 0), then which of the following points lie in the feasible region ?

$(\frac{1}{2}, \frac{5}{2})$

$\text{Corner points of feasible region: }(0,0),(0,4),(2,5),(6,3),(6,0).$

$\text{The feasible region is the polygon joining these points.}$

$(1)\;\left(\frac12,\frac{13}{2}\right)=(0.5,6.5)$

$y>5 \Rightarrow \text{lies above the region } \Rightarrow \text{Not feasible}.$

$(2)\;\left(\frac12,\frac52\right)=(0.5,2.5)$

$\text{This point lies inside the polygon} \Rightarrow \text{Feasible}.$

$(3)\;\left(\frac52,5\right)=(2.5,5)$

$\text{Above the line joining }(2,5)\text{ and }(6,3) \Rightarrow \text{Not feasible}.$

$(4)\;(5,5)$

$\text{Outside the upper boundary of the region} \Rightarrow \text{Not feasible}.$

$\text{Correct option: }(2)\;\left(\frac12,\frac52\right).$