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 PM.,or 11 PM., and each works an 8-hour shift. The following table shows the minimum number of workers neede the 6 periods into which the day is divided: during Decision vairable x, number of workers reporting for the start of working period i, where i-1, 2, 3, 4, 5, or 6 Period Time ???.-7A.M 7 A.M.-11 A.M. 11 A.M.-3 P.M. 3 P.M.-7 P.M 7 P.M. 11 PM 11 PM.- 3AM. Number of Servers Required 15 18 12 14 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, where i-1,2, 3, 4, 5, 6.) Objective function: MinimizeZ Subject to: X1215 X218 X3212 X4214 (7 A.M.-11 A.M.) (11 A.M. -3 PM.) (3 PM. -7 PM.) (7 P.M. -11 PM.) (11 PM.-3 A.M.) (3 AM. -7 A.M.) X6+23 For all X20

Explanation / Answer

Here the minimizing function is Z = x1 + x2 + x3 + x4 + x5 + x6

because as we needed to minixe the total work force working for the day.

by using constraints listed above with an additional constraint of each worker works for 8 hours a day

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