A1 Credit provides credit information to its customers throughout the country, 24 hours per day. Credit representatives answer customer calls and provide information. Based on demand patterns, the estimated number of representatives needed during four-hour time periods of each day are shown in the table.

                                        

Employees work shifts of eight consecutive hours, and shifts can start at the beginning of any of the six periods shown in the table. Assume this schedule will be repeated day after day, so that someone starting at 8 PM will contribute to the need for representatives in the midnight–4 AM time period. The supervisor has been instructed to schedule employees so that all demands can be met with a minimum possible number of employees.

(a) Formulate an LP to minimize the number of representatives needed.
(b) Set up and solve the problem on a spreadsheet.
(c) What is the optimal solution? Explain the rationale for the solution.