Initially the problem was posed as follows:
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 below. Union rules state that each full-time employee must work five consecutive days and then receive two days off. For example, an employee who works Monday to Friday must be off on Saturday and Sunday. The post office wants to meet its daily requirements using only full-time employees. Formulate and LP that the post office can use to minimize the number of full-time employees that must be hired.
Minimum # of full time employees required
Day 1 = Monday 17
Day 2 = Tuesday 13
Day 3 = Wednesday 15
Day 4 = Thursday 19
Day 5 = Friday 14
Day 6 = Saturday 16
Day 7 = Sunday 11
Hint: For variables, let Xi: # of employees beginning work on day i
However the Post Office now realizes that they have another option. On the weekends, they can hire part time workers to cover some of the demand. Part time workers only cost them 250 dirhams per day, whereas a full time worker costs them 300 dirhams per day (and they are committed to 5 days). Hence, if it were only a matter of economics, then they would use some part time workers on the weekends. However, in order to avoid serious quality problems, they restrict the number of part time workers to 40% of the total work needed on the weekends.
Develop a workforce plan for the post office.