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A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings?

Solve a linear programming problem where a student earns $10 per hour tutoring and $7 per hour as a teacher's aide, while having limited working hours. The problem involves maximizing weekly earnings under specific time constraints, applying concepts of linear inequalities and optimization.

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