The comer points of the feasible region for an L.P.P. are (0, 10), (5, 5), (5, 15) and (0, 30). If the objective function is $Z=\alpha x+\beta y, \alpha, \beta>0$, the condition on $\alpha$ and $\beta$ so that maximum of Z occurs at corner point (5, 5) and (0, 20) is:

$\alpha=3 \beta$

The correct answer is Option (3) → $\alpha=3 \beta$