Corner points of the bounded feasible region for an $LP$ problem are $(0,4), (6,0), (12,0), (12,16)$ and $(0,10)$. Let $z = 8x + 12y$ be the objective function. Match the following:
$(i)$ Minimum value of $z$ occurs at $\ldots$
$(ii)$ Maximum value of $z$ occurs at $\ldots$
$(iii)$ Maximum of $z$ is $\ldots$
$(iv)$ Minimum of $z$ is $\ldots$

• A
  $(i) (6,0), (ii) (12,0), (iii) 288, (iv) 48$
• B
  $(i) (0,4), (ii) (12,16), (iii) 288, (iv) 48$
• C
  $(i) (0,4), (ii) (12,16), (iii) 288, (iv) 96$
• D
  $(i) (6,0), (ii) (12,0), (iii) 288, (iv) 96$