Q13. A factory manufactures two types of screws, A and B, each type requiring the use of two machines an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on the hand-operated machine to manufacture a package of screws 'A', while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machine to manufacture a package of screws 'B'. Each machine is available for atmost 4 hours on any day. The manufacturer can sell a package of screws 'A' at a profit of Rs 7 and of screws 'B' at a profit of Rs 10. Assuming that he can sell all the screws he can manufacture, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit
