Bus drivers will needed during each of the next five years: 60 bus drivers in year 1; 70 Bus drivers in year 2; 50 Bus drivers in year 3; 65 Bus drivers in year 4; and 75 bus drivers in year 5. At the beginning of each year, the deans must decide how many Bus drivers should be hired or fired. It costs $4000 to hire a BUSDRIVER and $2000 to fire a BUSDRIVER. For continuity of the staff, the university will not fire more than 10% of the bus drivers in any year (e.g. at the start of year 3 it would not fire more than 10% of the bus drivers on staff during year 2). A bus drivers salary is $10,000 per 2 year. At the beginning of year 1, the university has 50 bus drivers. A BUSDRIVER hired at the beginning of a year may be used to meet the current years requirements and is paid full salary for the current year. Part-time bus drivers can also be hired and are paid proportionally to the amount of time they work (e.g. a bus driver who works 25% of a full load is paid 25% of a full salary). How many bus drivers should the university hire or fire at the beginning of each year to minimize total costs? How many bus drivers should it have on staff each year? What are the minimum total costs?

Please show me with math and by hand how to do this question so I can learn! Thank you!