Assume that each nurse works 8 consecutive hours at the Beaver Medical Center. The center has the following staffing requirements for each 4-hour work period.
If represents the number of nurses starting in period 1, the number starting in period 2, and so on, write and solve the linear programming problem that will minimize the total number of nurses needed. (Note that the nurses who begin work in period 6 work periods 6 and 1 for their 8-hour shift.)

A)The minimum 67 is nurses with 27 nurses starting in period 1, 5 nurses starting in period 2, 18 nurses starting in period 3, 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in period 6).
B)The minimum is 67 nurses with 27 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, 7 nurses starting in period 5, and 5 nurses starting in period 6 (no nurses need to start in period 2).
C)The minimum is 67 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6).
D)The minimum is 72 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 12 nurses starting in period 5 (no nurses need to start in periods 2 and 6).
E)The minimum is 62 nurses with 32 nurses starting in period 1, 13 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6).

Question

Assume that each nurse works 8 consecutive hours at the Beaver Medical Center. The center has the following staffing requirements for each 4-hour work period. ​  ​
If  represents the number of nurses starting in period 1,  the number starting in period 2, and so on, write and solve the linear programming problem that will minimize the total number of nurses needed. (Note that the nurses who begin work in period 6 work periods 6 and 1 for their 8-hour shift.)
​
A)The minimum 67 is nurses with 27 nurses starting in period 1, 5 nurses starting in period 2, 18 nurses starting in period 3, 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in period 6). 
B)The minimum is 67 nurses with 27 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, 7 nurses starting in period 5, and 5 nurses starting in period 6 (no nurses need to start in period 2). 
C)The minimum is 67 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
D)The minimum is 72 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 12 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
E)The minimum is 62 nurses with 32 nurses starting in period 1, 13 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6).

Quizplus · Accepted Answer

We can formulate the problem as follows:

Minimize: 
x1 + x2 + x3 + x4 + x5 + x6 (total number of nurses needed)

Subject to: 
x1 + x6 >= 13 (period 1)
x3 >= 9 (period 2)
x3 + x6 >= 18 (period 3)
x4 >= 10 (period 4)
x5 >= 7 (period 5)
x1 + x2 + x4 + x5 <= 47 (maximum number needed in any 4-hour period)

Note that we do not need to include a constraint for period 6, since any nurses starting in period 6 would also be counted in period 1.

Solving this linear programming problem using a solver or by hand, we obtain the minimum total number of nurses needed as 67, with the following assignment:

- 32 nurses start in period 1
- 18 nurses start in period 3
- 10 nurses start in period 4
- 7 nurses start in period 5

No nurses need to start in periods 2 and 6.

Therefore, the best choice is C.

Assume That Each Nurse Works 8 Consecutive Hours at the Beaver