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In a fire department unit in Toronto, firefighters work 24 hours each day. There are six shifts each day, so each day is divided into
In a fire department unit in Toronto, firefighters work 24 hours each day. There are six shifts each day, so each day is divided into six 4-hour periods. The minimum number of firefighters needed on each shift is illustrated below. Shift 1 Midnight- 4 AM Shift 2 4 AM-8 AM Shift 3 8 AM-Noon Shift 4 Noon-4 PM Shift 5 4 PM -8 PM Shift 6 8 PM -Midnight Number of Firefighters Needed 5 7 10 4 8 12 Firefighters must report to work at the beginning of the above time periods and must work twelve consecutive hours. Nonnegative decision variables X1, X2, X3, X4, X5, and X6 respectively represent the number of firefighters starting work at the beginning of shift 1, shift 2, shift 3, shift 4, shift 5, shift 6. With the objective to minimize the total number of firefighters working, which of the following models formulates the scheduling problem? Question 5 options: Minimize Total Number of firefighters= X1 + X2 + X3 + X4 + X5 + X6 Subject to X1 + X5 + X6 5 X1 + X2 + X6 7 X1 + X2 + X3 10 X2 + X3 + X4
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