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Problem 5, Page 953
All State University Business School faculty members are classified as tenured or untenured.
Each year, 10% of the untenured faculty are granted tenure and 10% leave State University; 95%
of the tenured faulty remain 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.
For what values of x does this goal require firing tenured faculty members? Describe a hiring
policy that maintains a faculty that is 10% untenured. Describe a hiring policy that maintains a
faculty that is 40% tenured.
Transition Matrix:
Untenured
Tenured
Leave
Untenured
.80
0
0
Tenured
.10
.95
0
Leave
.10
.05
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Hu= Hire Untenured
Ht= Hire Tenured
Lu= Left Untenured
Lt= Left Tenured
Bt= Become Tenured and Stay as Faculty
Hu = (20/100) x
Hu = .20x
Ht + (10/100) x = (5/100)(100-x)
Ht = 5 - 0.15x
If 0.15x ≤ 5 the faculty can maintain being 100 people.
If x = 10
Hu = 0.20(10) = 2 Ht = 5-0.15(10)= 3.5
If x = 40
Hu = 0.20(40) = 8 Ht = 5-0.15(40) = -1
Then for x=40 we need to fire a tenured faculty.
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