$2-$ Create a new sheet called "Manufacturing Analysis" and solve the following problem: $[20$ pts$]$

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