$A$ manufacturer makes two types of toys $A$ and $B$. Three machines are needed for this purpose and the time (in $minutes$) required for each toy on the machines is given below:

Types of Toys	Machine-$I$	Machine-$II$	Machine-$III$
$A$	$12$	$18$	$6$
$B$	$6$	$0$	$9$

Each machine is available for a maximum of $6 \, hours$ $(360 \, minutes)$ per day. If the profit on each toy of type $A$ is $Rs. \, 7.50$ and that on each toy of type $B$ is $Rs. \, 5$,find the number of toys of each type that should be manufactured in a day to get maximum profit.

• A
  $15 \, \text{toys of type } A, 30 \, \text{toys of type } B$
• B
  $20 \, \text{toys of type } A, 20 \, \text{toys of type } B$
• C
  $10 \, \text{toys of type } A, 40 \, \text{toys of type } B$
• D
  $30 \, \text{toys of type } A, 15 \, \text{toys of type } B$