$A$ manufacturer has three machines $I, II$ and $III$ installed in his factory. Machines $I$ and $II$ are capable of being operated for at most $12 \, hours$ whereas machine $III$ must be operated for at least $5 \, hours$ a day. She produces only two items $M$ and $N$ each requiring the use of all the three machines. The number of hours required for producing $1$ unit of each of $M$ and $N$ on the three machines are given in the following table:

Items	Machine $I$	Machine $II$	Machine $III$
$M$	$1$	$2$	$1$
$N$	$2$	$1$	$1.25$

She makes a profit of $Rs. \, 600$ and $Rs. \, 400$ on items $M$ and $N$ respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit?

• A
  $4$ units of $M$ and $4$ units of $N$,Maximum Profit $= Rs. \, 4000$
• B
  $6$ units of $M$ and $0$ units of $N$,Maximum Profit $= Rs. \, 3600$
• C
  $0$ units of $M$ and $6$ units of $N$,Maximum Profit $= Rs. \, 2400$
• D
  $5$ units of $M$ and $0$ units of $N$,Maximum Profit $= Rs. \, 3000$