# #2015_ 15 Mathematical modelling

**Algebra**Level 4

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?