Piecewise-Defined Functions

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1) Assume you work at a company where you are paid hourly. You are paid $8.60 per hour for regular time (less than or equal to forty hours) and time and a half for overtime hours up to, but not including, fifty hours in one week. If you are asked to work fifty or more hours in one week you are paid double-overtime. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working forty hours and for working forty-one hours. Post these values as well.
2) Assume you work at a company where you are paid hourly. You are paid $9.40 per hour for regular time (less than or equal to thirty hours) and time and a third for overtime hours up to, but not including, forty hours in one week. If you are asked to work forty or more hours in one week you are paid time and a half. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working thirty hours and for working thirty-one hours. Post these values as well.
3) Assume you work at a company where you are paid hourly. You are paid $7.80 per hour for regular time (less than or equal to thirty-five hours) and time and three-quarters for overtime hours up to, but not including, forty-five hours in one week. If you are asked to work forty-five or more hours in one week you are paid double-overtime. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working thirty-five hours and for working thirty-six hours. Post these values as well.
4) Assume you work at a company where you are paid hourly. You are paid $6.80 per hour for regular time (less than or equal to twenty hours) and double time for overtime hours up to, but not including, thirty hours in one week. If you are asked to work thirty or more hours in one week you are paid triple time. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working twenty hours and for working twenty-one hours. Post these values as well.

Question: Which job situation would pay the best overall for someone who works (on average) 30 hours per week? Which option would pay best for an employee who works (on average) 45 hours per week? Be sure to explain the reasoning for each answer.