The corner points of the bounded feasible region are $(0,0), (2,0), (4,2), (2,4)$ and $(0, \frac{10}{3})$. For the objective function $z = -x + 2y$:
$(i)$ Maximum value of $z$ is at $\ldots \ldots \ldots$
$(ii)$ Minimum value of $z$ is at $\ldots \ldots \ldots$
$(iii)$ The maximum value of $z$ is $\ldots \ldots \ldots$
$(iv)$ The minimum value of $z$ is $\ldots \ldots \ldots$

• A
  $(i) (2,4), (ii) (0,0), (iii) 6, (iv) 0$
• B
  $(i) (0, \frac{10}{3}), (ii) (4,2), (iii) 6, (iv) 0$
• C
  $(i) (2,4), (ii) (2,0), (iii) 6, (iv) -2$
• D
  $(i) (0, \frac{10}{3}), (ii) (2,0), (iii) \frac{20}{3}, (iv) -2$