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-4 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 mininnun 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.