Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. Larry has monitored the usage of the center at various times of the day, and determined that the following number of computer consultants are required:

Two types of computer 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 (noon-8 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.
Larry 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.
(a) Formulate a linear programming model for this problem.
(b) Solve this model by the simplex method.

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Minimum Number of Consultants Time of Day Required to Be on Duty 8 A.M.-noon Noon-4 P.M. 4 P.M.-8 P.M. 8 P.M.-midnight 4 8 10 6