Wichita\'s famous Sethi Restaurant is open 24 hours a day. Servers report for du

Question

Wichita's famous Sethi Restaurant is open 24 hours a day. Servers report for duty at 3 A.M., 7 A.M, 11 A.M., 3 PM., 7 P.M, or 11 P.M., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided: Decision vairable: X number of workers reporting for the start of working period I, where 1, 2, 3, 4, 5, or 6. Period Time 3 A.M. -7 A.M 7A.M. 11 A.M Number of Servers Requirec 15 18 12 14 3PM.-7 PM 7 PM.-11 PM 11 P.M.-3 A.M Owner Avanti Sethi's scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total staff required for one day's operation. (Hint Let X, equal the number of servers beginning work in time period i, wherei1, 2, 3, 4, 5, 6.) Objective function: Minimize z- Subject to: (7 A.M-11 A.M.) (11 A.M.-3 PM.) (3PM.-7 P.M.) (7 PM. -11 PM.) (11 PM. -3 A.M.) (???.-7A.M.) X12 15 X2218 X3212 XE 23 For all X,2 0

Explanation / Answer

Objective: Minimize Z = X1+X2+X3+X4+X5+X6

s.t.

X1+X2 >= 15

X2+X3 >= 18

X3+X4 >= 12

X4+X5 >= 14

X5+X6 >= 3

X6+X1 >= 3

Xi >= 0

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