CareMed, an HMO health care provider, operates a 24-hour outpatient clinic in Draperton, near the Tech campus. The facility has a medical staff with doctors and nurses who see regular local patients according to a daily appointment schedule. However, the clinic sees a number of Tech students, who visit the clinic each day and evening without appointments because their families are part of the CareMed network. The clinic has 12 nurses who work according to three 8-hour shifts.

Five nurses are needed from 8:00 a.m. to 4:00 p.m., four nurses work from 4:00 p.m. to midnight, and 3 nurses work overnight from midnight to 8:00 a.m. The clinic administrator wants to assign nurses to a shift according to their preferences and seniority (i.e., when the number of nurses who prefer a shift exceeds the shift demand, the nurses are assigned according to seniority). Although the majority of nurses prefer the day shift, some prefer other shifts because of the work and school schedules of their spouses and families. Following are the nurses’ shift preferences (where 1 is most preferred) and their years working at the clinic:

Shift Nurse 8 a.m. to 4 p.m. 4 p.m. to Midnight Midnight to 8 a.m. Years’ Experience Adams 1 2 3 2 Baxter 1 3 2 5 Collins 1 2 3 7 Davis 3 1 2 1 Evans 1 3 2 3 Forrest 1 2 3 4 Gomez 2 1 3 1 Huang 3 2 1 1 Inchio 1 3 2 2 Jones 2 1 3 3 King 1 3 2 5 Lopez 2 3 1 2 Formulate and solve a linear programming model to assign the nurses to shifts according to their preferences and seniority.