Question: THE SATURDAY SHIFT PROBLEM:

Tracey Ketchon, the manager of the Outrageous Rags Boutique is about to roster the Saturday three shift at her mall store. The twelve hour day is broken into three, four-hour shifts: 10AM to 2 PM, 2PM to 6PM, and 6PM to 10PM. Saturdays are her busy day; her requirements are as follows:

She has eight part-timers that could be selected. They are paid varying amounts depending on whether they are cashier trained and depending on their past sales. She would like to assign the clerks to the shift in a way that would maximize sales potential -- but not bust her payroll budget, which is $560. The part-timers, their sales volumes per four hour period, and whether or not they are cashier trained is as follows:

If a person is assigned to work on Saturday, they would need to be assigned for a full eight hours, with no split shifts, nor an assignment longer that eight hours. In addition, they will need at least one cashier-trained person on each shift.

There are several personnel problems. Hank and Denise are roommates and share Denise's car, and because of insurance problems, Hank can't drive Denise's car. Therefore, Hank can only work when Denise works. In addition, Charlotte hates Felicia, therefore you can't put them on the same shift. Finally, Tracey herself is off to the beach for the weekend and will not be working this Saturday.

Set up the LP algorithm to optimize the situation on the potential of maximizing sales, get the shift manned, and yet not break any of the constraints … and solve it via a computer output … show both the LP stubby pencil set up … the computer output … and then interpret the output back into the problem.