Problem

Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses):

Activity 1: Welcome a guest. (1 minute)

Activity 2: Clip and file nails. (3 minutes)

Activity 3: Paint. (5 minutes)

Activity 4: Dry. (10 minutes)

Activity 5: Check out the customer. (4 minutes)

Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3's constant attention; she/he needs to only escort the customer to the salon's drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon.

What is the average labor utilization of the servers (in decimal form)? Assume that there is unlimited demand and that the process only admits customers at the rate of the bottleneck.