$A$ dietician has to develop a special diet using two foods $P$ and $Q$. Each packet (containing $30 \, g$) of food $P$ 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 $Q$ 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. How many packets of each food should be used to minimise the amount of vitamin $A$ in the diet? What is the minimum amount of vitamin $A$?

• A
  $15$ packets of $P$,$20$ packets of $Q$; Minimum vitamin $A = 150$ units
• B
  $20$ packets of $P$,$15$ packets of $Q$; Minimum vitamin $A = 165$ units
• C
  $10$ packets of $P$,$25$ packets of $Q$; Minimum vitamin $A = 135$ units
• D
  $25$ packets of $P$,$10$ packets of $Q$; Minimum vitamin $A = 180$ units