$A$ dietician has to develop a special diet using two foods $X$ and $Y$. Each packet (containing $30 \ g$) of food $X$ contains $12$ units of calcium,$4$ units of iron,$6$ units of cholesterol and $6$ units of vitamin $A$. Each packet of the same quantity of food $Y$ contains $3$ units of calcium,$20$ units of iron,$4$ units of cholesterol and $3$ units of vitamin $A$. The diet requires at least $240$ units of calcium,at least $460$ units of iron and at most $300$ units of cholesterol. The corner points of the feasible region are:

• A
  $(2,72), (40,15), (15,20)$
• B
  $(2,72), (15,20), (0,23)$
• C
  $(0,23), (40,15), (2,72)$
• D
  $(2,72), (40,15), (115,0)$