A tire company makes two kinds of tires: Standard tires and Snow tires. Each tire is processed on three machines, A, B, and C. A standard tire requires a ½ hour on machine A, 2 hours on machine B, and 1 hour on C. A snow tire requires 1 hour on machine A, 1 hour on machine B, and 4 hours on C. During the next week, machine A will be available for at most 40 hours, Machine B for at most 100 hours, and machine C for at most 120 hours. The company makes $45 profit on standard tires and $75 profit on snow tires.