A manufacturer produces bicycles and motor cycles, each of which must be processed through two machine centers.

A manufacturer produces bicycles and motor cycles, each of which must be processed through two machine centers. Machine center 1 has a maximum of 120 hours available and machine 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 each bicycle and P2500 for a motorcycle, determine the number of bicycles and number of motorcycles to produce to maximize the profit, considering that the number of motorcycles must not exceed 12 units and bicycle must be at least 10 units.