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## Question

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From the Community

M R . K’S HAIR SALONMr. K’s is a very popular hair salon. It offers high-quality hair-styling and physicalrelaxation services at a reasonable price, so it always has unlimited demand. Theservice process includes five activities that are conducted in the sequencedescribed below. (The time required for each activity is shown in parenthesis):Activity 1: Welcome a guest and offer homemade herb tea. (10 minutes)Activity 2: Wash and condition hair. (10 minutes)Activity 3: Neck, shoulder, and back stress release massage. (10 minutes)Activity 4: Design the hairstyle and do the hair. (25 minutes)Activity 5: Check out the guest. (5 minutes)Three servers (S1, S2, and S3) offer the services in a worker-paced line. Theassignment of tasks to servers is the following:S1 does Activity 1.S2 does Activities 2 and 3.S3 does Activities 4 and 5.Q4. Assume a wage rate of $18 per hour. What are the direct labor costs for oneguest?To increase the service rate, Mr. K’s is considering two alternatives:Alternative I: To hire a new employee to help anyone (and only one) of theservers without changing the tasks performed by each server.Alternative II: To redesign the assignment of tasks to servers. For this, Mr. K’s isevaluating to reassign Activity 5 from S3 to S1Q5. What would be the costs of direct labor of serving one guest under each ofthe two alternatives? Assume that the system operates at its capacity and thereare no empty system effects.

## Answer

Solved

To answer the questions, we need to calculate the direct labor costs for serving one guest under the current setup and then evaluate the costs under each of the two proposed alternatives.

Current Setup

**Activity Times and Assignments:**- S1: Activity 1 (10 minutes)
- S2: Activities 2 and 3 (10 + 10 = 20 minutes)
- S3: Activities 4 and 5 (25 + 5 = 30 minutes)

**Wage Rate:**- $18 per hour

**Direct Labor Cost Calculation:**- Convert minutes to hours for each server:
- S1: 10 minutes = 10/60 hours
- S2: 20 minutes = 20/60 hours
- S3: 30 minutes = 30/60 hours

- Calculate cost for each server:
- S1: \( \frac{10}{60} \times 18 = 3 \) dollars
- S2: \( \frac{20}{60} \times 18 = 6 \) dollars
- S3: \( \frac{30}{60} \times 18 = 9 \) dollars

- Total cost per guest: \( 3 + 6 + 9 = 18 \) dollars

- Convert minutes to hours for each server:

Alternative I: Hire a New Employee

- Hiring a new employee to help one server does not change the tasks or time per guest, so the direct labor cost remains the same as the current setup: $18 per guest.

Alternative II: Reassign Activity 5 from S3 to S1

**New Assignments:**- S1: Activities 1 and 5 (10 + 5 = 15 minutes)
- S2: Activities 2 and 3 (20 minutes)
- S3: Activity 4 (25 minutes)

**Direct Labor Cost Calculation:**- Convert minutes to hours for each server:
- S1: 15 minutes = 15/60 hours
- S2: 20 minutes = 20/60 hours
- S3: 25 minutes = 25/60 hours

- Calculate cost for each server:
- S1: \( \frac{15}{60} \times 18 = 4.5 \) dollars
- S2: \( \frac{20}{60} \times 18 = 6 \) dollars
- S3: \( \frac{25}{60} \times 18 = 7.5 \) dollars

- Total cost per guest: \( 4.5 + 6 + 7.5 = 18 \) dollars

- Convert minutes to hours for each server:

Summary

**Current Setup Cost:**$18 per guest**Alternative I Cost:**$18 per guest**Alternative II Cost:**$18 per guest

Both alternatives result in the same direct labor cost per guest as the current setup.

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