Clancy's Casino, in Muledeer, Nevada, is open 24 hours a day, seven days a week. Along with all the other attractions and diversion, Clancy's operates a variety of gaming tables. Dealers at these tables are interchangeable.
The casino has the following daily requirements for dealers:
Time Minimum # of dealers
01:00 - 05:00 7
05:00- 09:00 4
09:00 - 13:00 9
13:00 - 17:00 12
17:00 - 21:00 15
21:00 - 01:00 17
A dealer may start work at the beginning of any one of the six shifts and, having begun, works eight consecutive hours.
A. Find the employee schedule that minimizes the total number of dealers required, meeting the minimum level of each shift's requirements.
B. Suppose in problem 4, Clancy's Casino pays a wage differential depending on the hours worked. In particular, between midnight and 0700, it pays dealers $16 per hour, between 0700 and 1900 $10 per hour, and between 1900 and midnight $12 per hour. Modify your formulation to problem 4, and determine the minimum cost shift schedule for Clancy's.