Formulation as a linear programming problem. Linear programming problems always involve finding the best mix of activity levels. The key to formulating this particular problem is to recognize the nature of the activities.
Activities correspond to shifts, where the level of Thus, this problem involves finding the best mix of shift sizes. Since the decision variables always are the levels of the activities, the five decision variables here are
Xj = number of agents assigned to shift j, for j = 1,2,3,4,5.