7. Scheduling LP Formulation A telephone call center operates from 7am to 6pm (MondayFriday) and uses hourly planning intervals for its scheduling decisions. The call center uses FT shifts that span a total of nine hours (eight hours of work and a one-hour meal break). The meal breaks in a FT shift can occur after the 3rd hour of work (3 hours of work, a one- hour break, and 5 hours of work), or after the fourth hour of work (4 hours of work, a onehour break, and 4 hours of work). The call center also uses PT shifts that consist of 4 consecutive hours of work with no break. Potential starting times for fulltime and parttime shifts are at the beginning of any hour, provided that the shift would not extend past the end of the operating day. The call center currently has 23 FT and 12 PT employees, which is sufficient to meet the daily requirements shown in the table below, so shortages in any hour are not permitted. The call center would like to assign the employees to shifts so as to minimize the maximum surplus [or excess labor] across the hours of the day (i.e. the largest surplus across all hours should be as small as possible). An additional constraint is that no more than three shift starting times can be used for the PT employees (note: the solution of the model should indicate what PT starting times to use don't just pick three). You have been asked to develop a linear programming formulation that will select the PT starting times and determine the assignment of PT and PT employees to shifts, so as to minimize the maximum surplus while satisfying labor requirements in each hour. Be sure to carefully identify your decision variables, objective function and constraints. [10 points] m