Determine the objective function then use the system of linear inequalities and its corner points to solve:

Bob earns $10 per hour for tutoring math students at the local high school. He earns $12 per hour as the TA at the local college to have sufficient time for all activities, bob can work no more than thirty Hrs per week as tutor or TA. High school needs that bob spend at least four hours per week in the tutoring center. This semester bob is the TA for the calculus class which has 1 hr recitation. Additionally to recitation, he should have at least one office hour per week and have time to grade but can't spend more than 20 hours per week on TA duties. How many hours must bob devote to every job to maximize the earnings? Find the maximum income per week?