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A factory manufactures two types of scre...

A factory manufactures two types of screws, `A` and `B`. Each type of screw requires the 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 screw `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 eách type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

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