Manpower Scheduling: (10') Ricbert is the chief bank teller of the Gringotts Wizarding Bank. He is responsible to schedule the staffing of the clerks for the bank. The bank opens from 8 A.M. until midnight. Ricbert has monitored the customers visiting the bank at various times of the day, and determined that the following number of clerks are required: Time of Day Minimum Number of Clerks Required to Be on Duty 8 A.M.-noon 4 Noon-4 P.M. 8 4 P.M.-8 P.M. 10 8 P.M.-midnight 6 Table 1.1: Minimum Number of Clerks Required for Each Time Period Two types of clerks can be hired: full-time and part-time. The full-time clerks 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 clerks are paid $40 per hour. Part-time clerks can be hired to work any of the four shifts listed in the above table (i.e., 8 A.M.-noon, noon-4 P.M., 4 P.M.-8 P.M. and 8 P.M.-midnight). Part-time clerks are paid $30 per hour. An additional requirement is that during every time period, the number of full-time clerks on duty cannot be strictly less than the number of part-time clerks on duty. Ricbert would like to determine how many full-time and how many part-time clerks should work each shift to meet all the above requirements at the minimum possible cost. Formulate the problem as a linear programming problem (ignoring the constraints that the number of clerks are required to be integers)