Question

task overview
task time day
1 12a - 4a tu
2 6p - 10p m
3 4a - 6:30a th
4 8p - 11p th

schedule
name days assigned shift
lei m, tu, w, th, f 4p - 11:30p
ava tu, w, th, f, sat 10p - 7a
dan w, th, f, sat 8p - 7a
zoe m, tu, w, th, f 11p - 5a

assign each employee to one task

Explanation:

Analyze the task requirements

We need to assign each of the four employees (Lei, Ava, Dan, Zoe) to exactly one of the four tasks (Task 1, Task 2, Task 3, Task 4) such that their assigned shift covers the task's time and day. Let's list the requirements for each task:

• Task 1: Tuesday (Tu), 12a - 4a (Midnight to 4:00 AM)
• Task 2: Monday (M), 6p - 10p (6:00 PM to 10:00 PM)
• Task 3: Thursday (Th), 4a - 6:30a (4:00 AM to 6:30 AM)
• Task 4: Thursday (Th), 8p - 11p (8:00 PM to 11:00 PM)

Using Tabular Analysis, we will match these tasks against employee schedules.

Analyze employee schedules

Let's look at each employee's available days and shift times:

• Lei:
• Days: M, Tu, W, Th, F
• Shift: 4p - 11:30p (4:00 PM to 11:30 PM)
• Ava:
• Days: Tu, W, Th, F, Sat
• Shift: 10p - 7a (10:00 PM to 7:00 AM next day)
• Dan:
• Days: W, Th, F, Sat
• Shift: 8p - 7a (8:00 PM to 7:00 AM next day)
• Zoe:
• Days: M, Tu, W, Th, F
• Shift: 11p - 5a (11:00 PM to 5:00 AM next day)

Match employees to tasks using logical deduction

Using Logical Deduction, we evaluate which employees can cover each task:

1. Task 2 (Monday, 6p - 10p):

• Only Lei and Zoe work on Mondays (M).
• Lei's shift is 4p - 11:30p, which fully covers 6p - 10p.
• Zoe's shift is 11p - 5a, which does not cover 6p - 10p.
• Therefore, Lei must be assigned to Task 2.

1. Task 4 (Thursday, 8p - 11p):

• Since Lei is assigned to Task 2, we look at the remaining employees who work on Thursday (Th) and cover 8p - 11p.
• Ava's shift is 10p - 7a (does not cover 8p).
• Zoe's shift is 11p - 5a (does not cover 8p).
• Dan's shift is 8p - 7a, which fully covers 8p - 11p on Thursday.
• Therefore, Dan must be assigned to Task 4.

1. Task 1 (Tuesday, 12a - 4a):

• This task is in the early morning of Tuesday (Midnight to 4:00 AM).
• An employee covering this must either start their shift late Monday night or work a shift covering these hours on Tuesday.
• Let's check Zoe: Zoe works Monday (M) starting at 11p until Tuesday 5a. This shift (Monday 11p - Tuesday 5a) fully covers Tuesday 12a - 4a.
• Let's check Ava: Ava works Tuesday (Tu) starting at 10p, which does not cover early Tuesday morning.
• Therefore, Zoe must be assigned to Task 1.

1. Task 3 (Thursday, 4a - 6:30a):

• This task is in the early morning of Thursday (4:00 AM to 6:30 AM).
• Ava works Wednesday (W) starting at 10p until Thursday 7a. This shift fully covers Thursday 4a - 6:30a.
• Therefore, Ava must be assigned to Task 3.

Verify the final assignments

Let's double-check that every employee has exactly one task and all constraints are met:

• **Zoe \(

ightarrow\) Task 1**: Monday shift (11p - 5a) covers Tuesday 12a - 4a. (Valid)

• **Lei \(

ightarrow\) Task 2**: Monday shift (4p - 11:30p) covers Monday 6p - 10p. (Valid)

• **Ava \(

ightarrow\) Task 3**: Wednesday shift (10p - 7a) covers Thursday 4a - 6:30a. (Valid)

• **Dan \(

ightarrow\) Task 4**: Thursday shift (8p - 7a) covers Thursday 8p - 11p. (Valid)

Answer:

The correct assignment for each employee is:

• Lei: Task 2
• Ava: Task 3
• Dan: Task 4
• Zoe: Task 1