Super City Discount Department Store is open 24 hours a day

Super City Discount Department Store is open 24 hours a day. The number of cashiers need in each four-hour period of a day is listed below.

Period Cashiers Needed 10 p.m. to 2 a.m. 8

2 a.m. to 6 a.m. 4

6 a.m. to 10 a.m. 7

10 a.m. to 2 p.m. 12

2 p.m. to 6 p.m. 10

6 p.m. to 10 p.m. 15

If cashiers work for eight consecutive hours, how many should be scheduled to begin working in each period in order to minimize the number of cashiers needed? Formulate the problem as a linear program with the following decision variables.

x1 = the number of cashiers who start at 10 PM.

x2 = the number of cashiers who start at 2 AM.

x3 = the number of cashiers who start at 6 AM.

x4 = the number of cashiers who start at 10 AM.

x5 = the number of cashiers who start at 2 PM.

x6 = the number of cashiers who start at 6 PM.

Solve the problem with Excel Solver. Report the minimum number of cashiers needed (i.e., objective function value).

Solution