A large department store operates 7 days a week. The manager estimates that the minimum number of salespersons required to provide prompt service is 12 for Monday, 18 for Tuesday, 20 for Wednesday, 28 for Thursday, 32 for Friday, and 40 for each of Saturday and Sunday. Each salesperson works 5 days a week, with the two consecutive off-days staggered throughout the week. For example, if 10 salespersons start on Monday, 2 can take their off-days on Tuesday and Wednesday, 5 on Wednesday and Thursday, and 3 on Saturday and Sunday. How many salespersons should be contracted, and how should their off-days be allocated?
Develop the linear programming model and determine how many salespersons should be contracted and how should their off-days be allocated.