A factory turns out two articles X and Y, each of which is processed by two machines P and Q. X requires 2 hours of P
and 4 hours of Q; Y requires 4 hours of P and 2 hours of Q. Note
that neither P nor Q can work more than 24 hours a day. If each
article X yields a profit of Rs. 30 and each article Y yields a
profit of Rs. 40, find how many of each article should be
produced daily for maximum profit. Also, find the maximum
profit.​