If the corner points of the feasible region for an L.P.P. are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function z = 4x + 6y occurs at

Given function is,

$\mathrm{z}=4\mathrm{x}+6\mathrm{y}$

At each point,

$\begin{array}{l}\mathrm{z}(0,2)=4\left(0\right)+6\left(2\right)\\ \mathrm{z}(0,2)=12\\ \mathrm{z}(3,0)=4\left(3\right)+6\left(0\right)\\ \mathrm{z}(3,0)=12\end{array}$

and $z(6,0)=4\left(6\right)+6\left(0\right)$

$\begin{array}{l}\mathrm{z}(6,0)=24\\ \mathrm{z}(6,8)=4\left(6\right)+6\left(8\right)\\ \mathrm{z}=24+48\\ \mathrm{z}(6,8)=72\end{array}$

and $z(0,5)=4\left(0\right)+6\left(5\right)$

i.e. $z(0,5)=30$

Therefore, min z occur at (0, 2) and (3, 0)

So we get the minimum value of Z occur at (0, 2) and (3, 0).