nursing hours question

Project Description:

a hospital needs to determine how many nurses to hire to cover a 24-hour period. the nurses must work 8 consecutive hours but can begin to work at the start of 6 different shifts. they are paid different wages depending on when they start their shifts. the number of nurses required per 4-hour time period and their wages are shown in the following table.
time period required # of nurses wage ($/hr)
12 am − 4 am 20 15
4 am − 8 am 30 16
8 am − 12 pm 40 13
12 pm − 4 pm 50 13
4 pm − 8 pm 40 14
8 pm − 12 am 30 15
let xi be the number of nurses working in time period i (i = 1,2,3,4,5,6) and disregard any integer requirements. formulate the lp model for this problem (hint: the lp has 6 constraints, not including nonnegativity).
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