Each day, workers at the Gotham City Police Department work two 6-hour shifts chosen from 12 A.M to 6 A.M., 6 A.M to 12 P.M., 12 P.M. to 6 P.M., and 6 P.M., to 12 A.m. The following number of workers are needed during each shift: 12 A.M to 6 A.M.---15 workers; 6 A.M to 12 P.M---5 workers; 12 P.M. to 6 P.M---12 Workers; 6 P.M., to 12 A.M---6 Workers. Workers whose two shifts are consecutive are paid $12 per hour; Workers whose shift are not consecutive are paid $18 per hour. Formulate an LP that can be used to minimize the cost of meeting the daily workforce.
Each day, workers at the Gotham City Police Department work two 6-hour shifts chosen from 12 A.M to 6 A.M., 6 A.M to 12 P.M., 12 P.M. to 6 P.M., and 6 P.M., to 12 A.m. The following number of workers are needed during each shift: 12 A.M to 6 A.M.---15 workers; 6 A.M to 12 P.M---5 workers; 12 P.M. to 6 P.M---12 Workers; 6 P.M., to 12 A.M---6 Workers. Workers whose two shifts are consecutive are paid $12 per hour; Workers whose shift are not consecutive are paid $18 per hour. Formulate an LP that can be used to minimize the cost of meeting the daily workforce.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 102P
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Each day, workers at the Gotham City Police Department work two 6-hour shifts chosen from 12 A.M to 6 A.M., 6 A.M to 12 P.M., 12 P.M. to 6 P.M., and 6 P.M., to 12 A.m. The following number of workers are needed during each shift: 12 A.M to 6 A.M.---15 workers; 6 A.M to 12 P.M---5 workers; 12 P.M. to 6 P.M---12 Workers; 6 P.M., to 12 A.M---6 Workers. Workers whose two shifts are consecutive are paid $12 per hour; Workers whose shift are not consecutive are paid $18 per hour. Formulate an LP that can be used to minimize the cost of meeting the daily workforce.
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