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Mathematics, 14.05.2021 03:40 avashon09
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
MIN X1 + X2 + X3 + X4
s. t. X1 + X4 ≥ 12 (on duty during shift 1)
X1 + X2 ≥ 15 (on duty during shift 2)
X2 + X3 ≥ 16 (on duty during shift 3)
X3 + X4 ≥ 14 (on duty during shift 4)
X1, X2, X3, and X4 ≥ 0
Given the optimal solution: X1* = 13, X2* = 2, X3* = 14, X4* = 0, how many workers would be assigned to shift 2?
a. 13
b. 12
c. 14
d. 15
e. 2
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