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# LP Scheduling problem

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A nursing home employs attendants who are needed around the clock. Each attendant is paid the same, regardless of when his or her shift begins. Each shift is 8 consecutive hours. Shift begin at 6 a.m., 10 am, 2 pm, 6 pm, 10 pm and 2 am. The following table shows the nursing home's requirements for the numbers of attendants to be on duty during specific time periods

a) what is the minimum number of attendants needed to satisfy the nursing home's requirements? b) The nursing home would like to use the same number of attendants determined in part (a) but would now like to minimize the total salary paid. Attendants are paid \$16 per hour during 8am-8pm, and a 25% premium per hour during 8pm- 8am. How should the attendants now be scheduled?

SHIFT TIME NUMBER OF ATTENDANTS

A 2-6 A.M. 8
B 6-10 A.M. 27
C 10 A.M.-2 P.M. 12
D 2-6 p.M. 23
E 6-10 P.M. 29
F 10-2 A.M. 23