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A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ and $Rs. 100$, respectively. The maximum profit per week of the firm is $Rs$._________

Type of machine Machining time required for the machine part (minutes) Maximum machining time available per week (minutes)
Turning machine $12$ $6$ $6000$
Milling center $4$ $10$ $4000$
Grinding Machine $2$ $3$ $1800$
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