2. The managers of the Frigid Midget Widget (FMW) Company, makers of small frozen widgets, have listed the tasks that must be completed to assemble one midget fiigid widget (see following table). The managers musidecide how large a crew toassignto each task; the size of the crew will determine the duration of the task (.g- enerally, there is an inverse relationship between crew size and job duration). Each job can be assigned a crew of minimum size, nomal size, or maximum size; no other choices are possible for technological reasons. In addition, union regulations require that an assigned crew cannot be changed for the duration of the task (e.g., they cannot assign a normal size crew for the first two days of a task and then increase the crew size for the remaining duration of the task). Task durations are merely equal to the total number of worker-days divided by the crew size assigned to the task. For example, if a normal crew is assigned to task

(1,2), then that task will require eight days to complete. The FMW Company has a contract to produce one fiigid widget every twenty-four days. Assuming that all workers can perform all tasks, determine how the production tasks should be scheduled in order to minimize the workforce needed (King and fing costs are very high in this industry).

Task (i, J] Total Worker-Days Minimum Normal Maximum