A company makes two kinds of tires: model R and model S. Each tire is processed on three machines, A,B, and C. To make one model R tire requires 1/2 hour on machine A, 2 hours on B, and an hour on C. To make one model S tire requires 1 hour on A, 1 hour on B, and 4 hours on C. During the next week, machine A will be available for at most 20 hours, machine B for at most 60 hours, and machine C for at most 60 hours. If the company makes a $10 profit on each model R and $15 profit on each model S tire, how many of each tire should be made to maximize the company's profit?

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