This case focuses on developing a deeper understanding of the personnel scheduling problem.

Big Town Fire Department would like to schedule their human resource requirements in fire and safety operations, aka, firefighters. The town runs two schedules per day, 12 hours each. Firefighters are compensated hourly at $30 per hour plus an additional 33% is added to this amount to pay for the benefits (health insurance, retirement, etc.) Firefighters who work the night shift received $5 more per hour and have a commensurate increase in their benefits cost.

The weekly firefighter personnel requirements are:

	Mon	Tues	Weds	Thurs	Fri	Sat	Sun
5a-5p	11	11	12	18	19	19	14
5p-5a	16	17	18	20	22	24	20

The "normal" shift for a firefighter is 4 days 12 hours a day followed by 3 consecutive days off, working on either the day or the night shift (but not both). In general the managers of Big Town would like to schedule the firefighters in the least cost way, but must make sure the requirements are met?

Suppose there is a limit on the total number of hours that part time firefighters can work. (Why might this be the case?) Suppose these limits are specified as follows: Part timers can work at most X% of the total hours worked in a week by ALL firefighters. Provide a table with different solutions and solution values for limits of 0%, 10%, 20%, 30%, 40%, of the total hours worked for part time firefighters as defined in part d. For example how does the schedule and associated cost look when the hours worked by part time firefighters is limited to be at most 20% of the total hour firefighter hours worked?