During each three-hour period, the Smalltown police force requires the following number of on-duty police officers: seven from midnight (i.e., 12 A.M.) to 3 A.M.; eight from 3 A.M. to 6 A.M.; five from 6 A.M. to 9 A.M.; six from 9A.M. to noon (i.e., 12 P.M.); five from noon to 3 P.M.; seven from 3 P.M. to 6 P.M.; and five from 6 P.M. to 9 P.M.; eight from 9P.M. to midnight. Each police officer works three consecutive three-hour shifts.
a. Determine how to minimize the number of police officers needed to meet Smalltown’s daily requirements.
b. Use SolverTable to see how the number of police officers changes as the number of officers needed from midnight to 3 A.M. changes from 3 to 15 with an increment of 1.