# A small store is open from 8:00 am to midnight and needs to be staffe

Question:

A small store is open from 8:00 am to midnight and needs to be staffed to meet the following requirements for each of four time periods:

 Time of the Day Minimum Number of Employees 8:00 to Noon 6 Noon to 4:00 pm 8 4:00 pm to 8:00 pm 12 8:00 pm to Midnight 6

The owner of the store can hire either full-time employees or part-time employees. Full-time employees work for 8 consecutive hours and hence can be hired for the following shifts: 8:00 am to 4:00 pm (Shift 1), Noon to 8:00 pm (Shift 2), 4:00 pm to Midnight (Shift 3). Each full-time employee is paid \$14 per hour. Part-time employees can be hired to cover any of the four time periods listed in the table above. Each part-time employee is paid \$12 per hour. In addition to the minimum number of employees (full-time or part-time) for each of the four time periods given above, the owner also wants to make sure that there are at least two full-time employees for every part-time employee on duty.

The owner wants to determine how many full-time and part-time employees to hire for each shift/time period that will minimize the overall cost.

1. What are are the decision variables and constraints?