A manufacturer produces bicycles and motorcycles each of which must be processed through 2 machine centers. Machine center 1 has a maximum of 120 hours available and machine center 2 has a maximum of 180 hours available. A bicycle requires 6 hours in machine center 1 and 3 hours in machine center 2. Manufacturing a motorcycle requires 4 hours in machine center 1 and 10 hours in machine center 2. If the profit is P450 for bicycle and P2000 for motorcycle, determine the number of bicycles and motorcycles to produce to maximize the profit.

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