Table 11.2
The daily requirements for highway patrol officers at Park City over the week are:
$$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline \text { Day } & \mathrm { M } & \mathrm { T } & \mathrm { W } & \mathrm { TH } & \mathrm { F } & \mathrm { S } & \mathrm { SU } \
\hline \text { Requirement } & 11 & 9 & 6 & 7 & 5 & 3 & 2 \
\hline
\end{array}$$
Each officer works five days a week and must have two consecutive days off.
-Use the information in Table 11.2.What is the minimum number of officers required if preference is given to the pair S-Su in case of a tie in the selection of off days?
A) 9
B) 10
C) 11
D) 12

Question

Table 11.2
The daily requirements for highway patrol officers at Park City over the week are:
 $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline \text { Day } & \mathrm { M } & \mathrm { T } & \mathrm { W } & \mathrm { TH } & \mathrm { F } & \mathrm { S } & \mathrm { SU } \
\hline \text { Requirement } & 11 & 9 & 6 & 7 & 5 & 3 & 2 \
\hline
\end{array}$$ 
Each officer works five days a week and must have two consecutive days off.
-Use the information in Table 11.2.What is the minimum number of officers required if preference is given to the pair S-Su in case of a tie in the selection of off days?
A) 9
B) 10
C) 11
D) 12

Quizplus · Accepted Answer

To minimize the number of officers required, we need to schedule each officer for five consecutive days of work. Therefore, we can start with Monday and schedule an officer for Monday, Tuesday, Wednesday, Thursday, and Friday. Then, we need to choose two consecutive off days for this officer. Since we prefer the pair S-Su, we can choose either Saturday and Sunday or Sunday and Monday as the off days. Without loss of generality, let's choose Saturday and Sunday as the off days.

Now, let's repeat this process for each day in the week. For Tuesday, we can schedule an officer for Tuesday, Wednesday, Thursday, Friday, and Saturday, with Sunday and Monday as off days. For Wednesday, we can schedule an officer for Wednesday, Thursday, Friday, Saturday, and Sunday, with Monday and Tuesday as off days. For Thursday, we can schedule an officer for Thursday, Friday, Saturday, Sunday, and Monday, with Tuesday and Wednesday as off days. For Friday, we can schedule an officer for Friday, Saturday, Sunday, Monday, and Tuesday, with Wednesday and Thursday as off days. For Saturday, we can schedule an officer for Saturday, Sunday, Monday, Tuesday, and Wednesday, with Thursday and Friday as off days. Finally, for Sunday, we can schedule an officer for Sunday, Monday, Tuesday, Wednesday, and Thursday, with Friday and Saturday as off days.

Therefore, we need at least one officer for each day of work. This gives a total of 7 officers. However, we also need to account for the fact that each officer can only work five days a week. Therefore, we need to divide the work days by the number of work days per officer:

11 + 9 + 6 + 7 + 5 + 3 + 2 = 43
43 / 5 = 8.6

Since we can't have a fractional number of officers, we need to round up to the next integer. Therefore, we need at least 9 officers. However, if there is a tie in the selection of off days, we need to give preference to the pair S-Su. The only tie occurs for officers scheduled for Thursday, Friday, Saturday, Sunday, and Monday. For these officers, we need to choose Sunday and Monday as the off days to satisfy the S-Su preference.

Therefore, we need at least 9 officers, and the correct answer is (C) 11.

Table 112 the Daily Requirements for Highway Patrol Officers at Park

Table 112
the Daily Requirements for Highway Patrol Officers at Park