ASU has decided to open a call center. They will need people to work 8h shifts and go 24h/day (3 shifts/day, 1^st, 2^nd, 3^rd). A demand schedule was worked out as follows:

Shift	Mon	Tue	Wed	Thu	Fri	Sat	Sun
1st	7	8	9	5	7	2	5
2nd	5	3	2	4	3	2	2
3rd	9	10	10	7	11	2	2

The following conditions were adopted for workers:

Each worker works four consecutive days during any seven day period.

Each worker is assigned to worka shift (1^st, 2^nd, 3^rd) and once a worker has been assigned to a shift they must remain on the same shift every day that they work.

The number of workers for every shift, every day is a constant. ASU does not want to pay for extra workers and being short-handed is also not acceptable.

1. How many different kinds of 4 day shifts can there be? Write them out.
2. Considering the demand schedule, what is the minimum number of workers needed to fill out the schedule?
3. Is there a weakness in the LP result that you derived?