$A$ manufacturing company makes two models $A$ and $B$ of a product. Each piece of Model $A$ requires $9$ labour hours for fabricating and $1$ labour hour for finishing. Each piece of Model $B$ requires $12$ labour hours for fabricating and $3$ labour hours for finishing. For fabricating and finishing,the maximum labour hours available are $180$ and $30$ respectively. The company makes a profit of Rs $8000$ on each piece of model $A$ and Rs $12000$ on each piece of Model $B$. How many pieces of Model $A$ and Model $B$ should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

• A
  $12$ pieces of $A$,$6$ pieces of $B$; Max Profit = Rs $1,68,000$
• B
  $6$ pieces of $A$,$12$ pieces of $B$; Max Profit = Rs $1,68,000$
• C
  $10$ pieces of $A$,$10$ pieces of $B$; Max Profit = Rs $2,00,000$
• D
  $20$ pieces of $A$,$0$ pieces of $B$; Max Profit = Rs $1,60,000$