2. A city police department has the following minimal daily requirement for policeman. Note, you are to consider period 1 as following immediately after period 6. Each policeman works eight consecutive hours. Let X denote the number of officers starting work in period t everyday. The police department seeks a daily manpower schedule that employs the least number of policemen, provided that each of the above requirements is met. Formulate linear programming model to find an optimal schedule. Time of Day Period Minimal number of police required during a period 2-6 1 20 6 - 10 2 50 10-14 3 80 14-18 4 100 18 - 22 5 40 22 - 2 6 30