All state University Business School faculty members are cla

All state University Business School faculty members are classified as tenured or untenured. Each year, 10% of the untenured faculty is granted tenure and 10% leave Sate University; 95% of the tenured faculty remains and 5% leave. The business school wants to maintain a faculty with 100 members, of which x% are untenured.

Determine a hiring policy that will achieve this goal.

a) For what values of x does this goal require firing tenured faculty members?

b) Describe a hiring policy that maintains a faculty that is 10% untenured.

c) Describe a hiring policy that maintains a faculty that is 40 % untenured

Solution

Let there be x out of 100 untenured members. Thus, there are (100-x) tenured members. Hence, each year 0.10x untenured and (5-0.05x) tenured members leave. Therefore, to mantain a faculty of 100 members, the School will have to hire as many members as they leave, i.e. the School would have to hire (5-0.05x+0.10x) members, i.e. (5+0.05x) members.

a. The School would have to fire tenured members only when it would be greater than (100-x). This would happen when x is greater than or equal to 40. When there are 40 untenured and 60 tenured members, at the end of the year, 0.05*60=3 tenured members would leave and 0.10*40=4 untenured members would be granted tenure. Thus there would be 61 tenure members, and the School would need to fire a tenure member.

b. Hiring policy that maintains a faculty that is 10% untenured is hiring (5+0.05*10) =5.5 round 6 members.

c. Hiring policy that maintains a faculty that is 40 % untenured is hiring (5+0.05*40) =7 members