However, their union contract requires that waiters be hired to work five consecutive days in each week. The restaurant may decide which five consecutive days a waiter works and which two consecutive days he or she has off.
The restaurant's goal is to meet the demand with as few waiters as possible. On days there are extra waiters, they can work on related tasks like filling salt shakers.
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The Answer Report shows us the solution is not degenerate; there are seven decision variables (identified by which five consecutive days each waiter works) and there are seven binding constraints (including five binding nonnegativity constraints and the required staffing for Friday and for Saturday.)
The sensitivity analysis has some interesting features. Every decision variable has an objective coefficient of 1 and the allowable increases and decreases for them are meaningless since it makes no sense to call one waiter anything but one waiter.
But it is important to note that some of the work schedules have a "final value" of zero and also a "reduced cost" of zero. The meaning of this is that if we added a constraint that a few people work this schedule, there would be no additional cost. This gives the manager some flexibility in assigning individuals. But the Monday-Friday schedule and the Sunday-Thursday work schedule have nonzero reduced cost; the manager cannot assign waiters to these schedules without a cost, since these are the two schedules that are off work on Saturday, the busiest day of the week.
The sensitivity analysis for constraints tells us which days of the
week we could increase staffing requirements at no extra cost, and which days
cutting the requirement would save us money.