A local manufacturing plant runs 24 hours a day , 7 days a week. During various

Question

A local manufacturing plant runs 24 hours a day , 7 days a week. During various hours times throughout the day different numbers of workers are needed to run the various machines. Below are the minimum number of people needed to safely run the plant during a 24 hour period. Each worker works two consecutive 4-hour period. Formulate an LP that the plant manager can use to find the minimum number of workers needed to safely run the plant.

Time # of workers needed

12am-4am 8

4am-8am 9

8am-12pm. 15

12pm-4pm 14

4pm-8pm 13

8pm-12pm. 11

Explanation / Answer

Let Xi = the number workers beginning work at the start of time period i (i=1,2,3,4,5,6).

Minimize X1 + X2+ X3+ X4+ X5+ X6

Subject to

X1+ X6>=8

X1+ X2>=9

X2+ X3>=15

X3+ X4>=14

X4+ X5>=13

X5+ X6>=11

X1 , X2, X3,X4, X5,X6>=0.

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