Question

The daily requirements for patrol officers are: M T W TH F SA SU

4 5 6 7 10 9 9

Question: Each officer works 5 days a week and must have 2 consecutive days off. You are scheduling officers to work the appropriate days of the week. The second officer you schedule is to work which days of the week?

Answer 1

As given, the daily requirements for patrol officers are

M	T	W	TH	F	SA	SU
4	5	6	7	10	9	9

In the first step, we will assign work days to first worker. Identify the two consecutive days with the lowest numbers and these will be days off for first worker. Looking at the requirement, Monday and Tuesday have lowest requirement so for first worker M and T will be days off. We will highlight this as below.

M	T	W	TH	F	SA	SU
4	5	6	7	10	9	9

Now, for second worker we will substract from each of the work days for worker 1 except the highlighted days of day off for worker as shown below. This indicates that one less worker is requirement from W to Su as first worker is already assigned to these days.

M	T	W	TH	F	SA	SU
4	5	6-1=5	7-1=6	10-1=9	9-1=8	9-1=8

Again, for second workers, the lowest pair is M-T for days off. So, the second worker will also work from W till Su.

Hence, the second officer schedule is to work on W, TH, F, SA, SU.

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