A bus company believes that it will need the following numbers of bus drivers during each of the next 5 years:
60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; 75 drivers in year 5. At the beginning of each year, the bus company must decide how many drivers to hire or fire. It costs $4000 to hire a driver and $2000 to fire a driver. A driver's salary is $10,000 per year. At the beginning of year 1 the company has 50 drivers. A driver hired at the beginning of a year can be used to meet the current year's requirements and is paid full salary for the current year.
a. Determine how to minimize the bus company's salary, hiring, and firing costs over the next 5 years.