Please help me with this operations management question:
A university believes that it will need the following number ofcontract 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 manyCIs should be hired or fired. It costs $4000 tohire a CI and $2000 to fire a CI.
For continuity of the staff, the university will notfire more than 10% of the CIs in any year (e.g. at thestart of year 3 it would not fire more than 10% of the CIs on staffduring year 2).
A CI’s salary is $10,000 per 2 years.
At the beginning of year 1, the university has 50CIs.
A CI hired at the beginning of a year may be used to meet thecurrent year’s requirements and is paid full salary for the currentyear. Part-time CIs can also be hired and are paid proportionallyto the amount of time they work (e.g. a CI who works 25% of a fullload is paid 25% of a full salary).
How many CIs should the university hire or fire at the beginningof each year to minimize total costs? How many CIs should it haveon staff each year? What are the minimum total costs?