# #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?

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