Table 8-4
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 X 1 - X 4 represent the number of employees starting work on each shift (shift 1 through shift 4).
-According to Table 8-4, which describes a labor planning problem and its solution, how many workers would actually be on duty during shift 1?
A) 12
B) 13
C) 0
D) 29
E) None of the above

Question

Table 8-4
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 X 1 - X 4 represent the number of employees starting work on each shift (shift 1 through shift 4). 
-According to Table 8-4, which describes a labor planning problem and its solution, how many workers would actually be on duty during shift 1?
A) 12 
B) 13 
C) 0 
D) 29 
E) None of the above

Quizplus · Accepted Answer

Looking at the constraints in Table 8-4, we can see that 13 employees are required at the start of shift 1. This is confirmed by looking at the optimal solution in the table, which shows X₁ = 13. Therefore, the correct answer is B) 13.

Table 8-4 The Following Is a Linear Programming Formulation of a Labor