Problem
Suppose one wish to schedule shifts for safety workers, such as police or fire personnel. The goal is to minimize the cost of paying these workers while ensuring that there are enough workers available for safety calls at any given time. There are requirements to covered each time period, that is, each hour of the day. Each worker has a known, fixed hourly cost for each hour they are scheduled to work. The decision variables will be xij = 1 if worker i is assigned to shift j and 0 if worker i is not assigned to shift j. If linear programming is used to solve this problem, which assumption(s) might be violated?