A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the following table.
Days of week # of full-time employees required
1 = Monday 17
2 = Tuesday 13
3 = Wednesday 15
4 = Thursday 19
5 = Friday 14
6 = Saturday 16
7 = Sunday 11
Union rules state that each full-time employee must work five consecutive days and than receive two days off. Further suppose that the post office can force employees to work one day of overtime each week. For example, and employee whose regular shift is Monday to Friday can also be required to work on Saturday. Each employee is paid $50 a day for each of the first five days worked during a week and $62 for the overtime day (if any). Formulate an LP whose solution will enable the post office to minimize the cost of meeting its weekly work requirements.