Please help me with this operations management question:

A university believes that it will need the following number of contract instructors (CIs) during each of the next five years:

60 CIs in year 1

70 CIs in year 2

50 CIs in year 3

65 CIs in year 4

75 CIs in year 5.

At the beginning of each year, the deans must decide how many CIs should be hired or fired. It costs $4000 to hire a CI and $2000 to fire a CI.

For continuity of the staff, the university will not fire more than 10% of the CIs in any year (e.g. at the start of year 3 it would not fire more than 10% of the CIs on staff during year 2).

A CIs salary is $10,000 per 2 years.

At the beginning of year 1, the university has 50 CIs.

A CI 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 CIs can also be hired and are paid proportionally to the amount of time they work (e.g. a CI who works 25% of a full load is paid 25% of a full salary).

How many CIs should the university hire or fire at the beginning of each year to minimize total costs? How many CIs should it have on staff each year? What are the minimum total costs?