8. (10 marks total) Downtown Cabs has 70 drivers who may work 8-hour shifts from midnight to 8am, 4am to noon, 8am to 4pm, noon to 8pm, 4pm to midnight and 8pm to 4am. The slowest period is between midnight and 4am: a driver will average $80 in fares during that period. The largest fares result from the morning airport runs - drivers who start their shift at 4am will average $500 in fares, while those who start at 8am average $420. Drivers who start at noon average $300, and drivers who start at 4pm average $270. Drivers who start at 8pm earn an average of $210 in fares during their 8 hour shift. To retain a high level of customer service, the company has determined the minimum number of drivers necessary during the following 4-hour intervals - 10 from midnight to 4am, 12 from 4am to 8am, 20 from 8am to noon, 25 from noon to 4pm, 32 from 4pm to 8pm, and 18 from 8pm to midnight. a) Formulate (but do not attempt to solve) a model to help Downtown Cabs best schedule their drivers. Define all variables carefully. (7 marks) b) If only 15 drivers are available to work between midnight and 8am, how does the model change? (2 marks) c) The most popular day shift for drivers to work is from 8am to 4pm. Consequently, the company has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate the model to reflect this restriction. (1 mark)