Assignment:
In a small suburban town, firefighters work 8-hour shifts. Assume there are 6 shifts each day that are divided into six 4-hour periods. The minimum number of firefighters needed on each shift is illustrated below.
Shift Number of Firefighters Needed
Midnight - 4 a.m. 5
4 a.m - 8 a.m. 6
8 a.m.- Noon 10
Noon - 8 p.m. 12
4 p.m.- 8 p.m. 8
8 p.m.- Midnight 5
Firefighters must report to work at the beginning of the above time periods and must work eight consecutive hours.
Formulate the given problem scenario as a linear program so as to determine the minimum number of firefighters needed on each shift. Solve the problem using Microsoft Excel Solver. For the formulation, provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible. Also, the Excel setup should provide clearly labeled values used for the decision variables, constraints, and objective function.