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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 33% for benefits. Firefighters who work the night shift received $5 more per hour and have a commensurate increase in benefits. The weekly firefighter personnel requirements are: Mon Tues Weds Thurs Fri Sat Sun 5a-5p 11 13 15 19 15 13 9 5p-5a 17 13 15 17 19 21 14 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 (not both). Big Town managers would like to schedule the firefighters in the least cost way, but must make sure the requirements are met? Questions to Address a. Provide a table with different solutions for upper limits of 0%, 20%, 40%, etc., of part time firefighters as defined in part d (not part c). For example, assume that at most the total number of firefighters who are part time is 20% of the total number and so on. b. What if the total number of firefighters are limited due to turnover or other challenges in hiring? Starting from the benchmark solution, limit the total number of firefighters by 1, 2, 3, ..., 10. To enable finding an answer, allow the firefighters to work "double" shifts (day and night), and pay the double-shift employees "time and a half" for their work on all hours over 48 hours per week. Report the implications in terms of cost. Note 1: If the benchmark solution had 22 firefighters in total (not the actual answer), then, the goal here would be to find the best schedule with 21 firefighters, with some overtime involved. Then repeat for 20, 19, etc. Note 2: To include shifts that allow for overtime, you may need to make some assumptions about how much overtime is permitted for a firefighter per week. How safe is it if firefighters are working too much? c. Summarize and generalize the findings in this case