$7-$ A lean system has $22$ containers, each of which can hold $15$ parts. The lead time required to round$-$trip one container through the system is four hours. The required safety stock is ten percent.

a$)$ What is the maximum demand rate this system can accommodate?

b$)$ The company wants to accommodate double the maximum demand rate found in a$)$ What are all the ways the system could be changed to accomplish this?

$8-$ Jim Corner, owner of Corner Bike Rentals, wants to start analyzing his company's quality. For each bike rental, there are four types of customer complaints: bike not working properly, bike wrong size, bike uncomfortable, and bike broken during operation. During the past week, his company rented $280$ bikes. He received $26$ total complaints.

a$.$ What is his company's DPMO for the past week?

b$.$ What is their Six Sigma operating level?

c$.$ If Jim wanted to operate at the $5$ sigma level, what would his errors have needed to be over the past week?