#2015_ 15 Mathematical modelling

A manufacturer of medicines is preparing a production plan of medicines ${ M }_{ 1 }$ and ${ M }_{ 2 }$ . There are sufficient raw materials available to make $20000$ bottles of ${ M }_{ 1 }$ and $40000$ bottles of ${ M }_{ 2 }$ , but there are only $45000$ bottles into which either of the medicines can be put. Further , it takes $3 hours$ to prepare enough material to fill $1000$ bottles of ${ M }_{ 1 }$ , it takes $1 hour$ to prepare enough material to fill $1000$ bottles of ${ M }_{ 2 }$ and there are $66$ hours available for this operation. The profit is $Rs 8$ per bottle for ${ M }_{ 1 }$ and $Rs 7$ per bottle for ${ M }_{ 2 }$ . What is the maximum profit he can achieve?

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