The director of a call center needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. The director has monitored the usage of the center at various times of the day, and determined that the following numbers of consultants are required:

Two types of consultants can be hired: full-time and part-time. The full-time consultants work for 8 consecutive hours in any of the following shifts: morning (8 A.M.4 P.M.), afternoon (noon8 P.M.), and evening (4 P.M.midnight). Full-time consultants are paid $40 per hour. Part-time consultants can be hired to work any of the four shifts listed in the above table. Part-time consultants are paid $30 per hour. An additional requirement is that during every time period, there must be at least 2 full-time consultants on duty for every part-time consultant on duty. The director would like to determine how many full-time and how many part-time workers should work each shift to meet the above requirements at the minimum possible cost. Formulate a linear programming model for this problem.

\begin{tabular}{|l|l|} \hline Time of Day & Minimum Number of Consultants Required \\ \hline 8 a.m.-Noon & 4 \\ \hline Noon-4 p.m. & 8 \\ \hline 4 p.m. -8 p.m. & 10 \\ \hline 8 p.m.-Midnight & 6 \\ \hline \end{tabular}