$A$ company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type $A$ require $5 \text{ minutes}$ each for cutting and $10 \text{ minutes}$ each for assembling. Souvenirs of type $B$ require $8 \text{ minutes}$ each for cutting and $8 \text{ minutes}$ each for assembling. There are $3 \text{ hours } 20 \text{ minutes}$ available for cutting and $4 \text{ hours}$ for assembling. The profit is $Rs. 5$ each for type $A$ and $Rs. 6$ each for type $B$ souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?
- A$8$ of type $A$ and $20$ of type $B$
- B$20$ of type $A$ and $8$ of type $B$
- C$10$ of type $A$ and $15$ of type $B$
- D$15$ of type $A$ and $10$ of type $B$
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