OC Transpo believes that it will need the following number of LRT drivers during each of the next
five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; and 75 drivers in year 5. At the beginning of each year, the company must decide how many drivers should be hired or fired. It costs $40,000 to hire a driver and $20,000 to fire a driver. For continuity of the staff, the company will not fire more than 10% of the drivers in any year (e.g. at the start of year 3 it would not fire more than 10% of the drivers on staff during year 2). A driver's salary is $100,000 per year. At the beginning of year 1, the company has 50 drivers. A driver hired at the beginning of a year may be used to meet the current year's requirements and is paid full salary for the current year. Part-time drivers can also be hired and are paid proportionally to the amount of time they work (e.g. a driver who works 25% of a full load is paid 25% of a full salary). How many drivers should the company hire or fire at the beginning of each year to minimize total costs? How many drivers should it have on staff each year? What are the minimum total costs?
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