PCC store needs anything between 22 to 30 workers depending on the time of the day. The rush hours are between 12:00 PM (noon) and 2:00 PM. The table indicates the number of workers needed at various hours when the store is open.

Time Period	Number of Workers needed
9:00 AM to 11:00 AM	22
11:00 AM to 1:00 PM	30
1:00 PM to 3:00 PM	25
3:00 PM to 5:00 PM	23

PCC now employs 24 full-time workers but also needs a few part-time workers. A part-time worker must put in exactly 4 hours per day, but they can start any time between 9 AM and 1 PM. Full-time workers work from 9:00 AM to 5:00 PM but are allowed an hour for lunch (half of the full-timers eat at noon, the other half at 1:00 PM. Full-timers thus provide 35 hours per week of productive labor time.

The management of the PCC limits part-time hours to a maximum of 50% of the days total requirement. Part-timers earn $28 per day on average, while full-timers earn $90 per day in salary and benefits on the average. The management wants to set a schedule that would minimize total manpower costs. They can layoff full-time workers if needed but they would not hire any more full-time workers.

Formulate this problem as a mathematical model to minimize total daily manpower cost. Clearly state the decision variables, objective function, and constraints. (No need for Excel Solver Solution)