Problem 1[15 pts.]:Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assembly of the bike requires completing seven tasks. Tasks need to be performed in the sequence 1 to 7. Task times are summarized here:

Task	Description	Time (seconds)
1	The plastic tube for the frame is cut to size	30 seconds
2	The tube is put together	20 seconds
3	The frame is glued together	35 seconds
4	The frame is cleaned	25 seconds
5	Paint is sprayed onto the frame	30 seconds
6	Wheels are assembled	45 seconds
7	All other parts are assembled to the frame	40 seconds

Under the current process layout, workers are allocated to the tasks as shown here:

• Worker 1: Tasks 1 and 2
• Worker 2: Task 3
• Worker 3: Tasks 4 and 5
• Worker 4: Task 6
• Worker 5: Task 7

Assume the workers are paid $15 per hour. Each bicycle is sold for $6 and includes parts that are sourced for $1. The company has fixed costs of $200 per hour. There exists substantially more demand for the bicycle than Atlas can supply.

a. What is the hourly capacity of the line with 5 workers and the current layout?

b. What is the average labor utilization of 5 workers if the line is producing 60 per hour?

c. How much profit does the company make per hour if producing 60 per hour?

d.The company is considering hiring one more worker, which will increase the number of workers from 5 to 6. By how much will the hourly capacity change by hiring one more worker? Show the optimal allocation of tasks to different workers.