The School of Business at Hop Jonkins University (HJU) has received authorization from the university president to hire up to 20 new full-time faculty members and spend up to $1,200,000 a year in new salaries. The school is seeking professors at all levels: assistant, associate, and full professor.
The dean has authorized that at least 50% of the new faculty who are hired should be assistant professors, and at least 70% of the new faculty hired should be below the rank of full professor. In addition, at least three full professors must be hired.
The following table gives the average salaries and years of experience for professors in each of the three ranks. The school is interested in hiring the most qualified mix of faculty (as measured by the total combined years of experience) that meets the stated constraints.
Rank Average Salary Average Years of Experience
Assistant $55,000 2
Associate $69,885 7
Full $93,470 14
a) Formulate a linear program for the scenario described above.
b) Critique your model in part (a) against the four main assumptions of linear programming. Do you think a linear program is an appropriate model for this problem? Explain your answer.