Q2. [10 marks] You may use a solver such as LINDO to solve the following problem. A university believes that it will need the following number of contract instructors (Cls) during each of the next five years: 60 ls in year 1; 70 Cls in year 2; 50 Cls in year 3; 65 Cls in year 4; and 75 Cls in year 5. At the beginning of each year, the deans must decide how many Cls should be hired or fired. It costs $4000 to hire a Cl and $2000 to fire a Cl. For continuity of the staff, the university will not fire more than 10% of the Cls in any year (e.g. at the start of year 3 it would not fire more than 10% of the Cls on staff during year 2). A Cl's salary is $10,000 per 1 year. At the beginning of year 1, the university has 50 Cls. A CI 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 Cls can also be hired and are paid proportionally to the amount of time they work (e.g. a Cl who works 25% of a full load is paid 25% of a full salary). How many Cls should the university hire or fire at the beginning of each year to minimize total costs? How many Cls should it have on staff each year? What are the minimum total costs