Table 1. Police Requirements Time of Day Number of Officers Required 2:00 a.m. -- 6:00 a.m. 6:00 a.m. -- 10:00 a.m. 6 10:00 a.m. -- 2:00 p.m. 8 2:00 p.m. -- 6:00 p.m. O 6:00 p.m. -- 10:00 p.m. 4 10:00 p.m. -- 2:00 a.m. 6 Officers report for duty at the start of each of the above six time periods and remain on duty for eight consecutive hours. The pay of the officers varies slightly depending of the time of day. From 6:00 a.m. until 10:00 p.m. officers are paid $18 per hour. From 10:00 p.m. until 6:00 a.m. officers are paid $20 per hour. a) Formulate and solve a linear program that the police station can use to minimize the cost of the police officers it must hire to meet its needs throughout the day. Write the algebraic formulation clearly by defining all decision variables and mathematically expressing the objective function and constraints. (Hint: A similar problem appears in the textbook )