A company needs to schedule the staffing of one of its offices, which is open from 8am to midnight, at a minimum cost. The number of clerks needed is as follow:
Time of day Minimum number of clerks
8am - noon 4
Noon - 4pm 8
4pm - 8pm 10
8pm - midnight 6
Two types of clerks can be hired: part-time and full-time. Part-time clerks can be hired to work on any of the four shifts listed above; they earn $11/hr. Full-time clerks work for 8 consecutive hours in any of the following shifts: 8am - 4pm, noon - 8pm, and 4pm - midnight. Full time clerks earn $15/hr. An additional requirement is that during any time period there must be at least 2 full-time clerks on duty for every part-time clerk.

Set up a linear programming model that corresponds to this staffing problem, clearly:

Define your decision variables

Define your objective function, and

Describe the scheduling restriction represented by each constraint equation.