The manager of a computer help center needs to determine a shift schedule for his sta . The center is open from 8am until midnight (12am), and is divided into four shifts. The number of employees needed on each shift is as follows: 4 on the rst shift (8am-12pm), 10 on the second shift (12pm-4pm), 8 on the third shift (4pm-8pm), and 6 on the last shift (8pm-12am). Two types of employees can be hired to sta the computer center: full-time employees and part-time employees. Full-time employees must be hired for two consecutive shifts, and can be hired to start in the rst, second or third shift. Part-time employees are hired for a single shift. Full-time employees are paid $14 an hour, while part-time employees are paid $12 an hour. Lastly, during each of the shifts, there must be at least two full-time employees sta ed for every part-time employee.
Formulate a linear programming model to satisfy the stang requirements at minimum cost.