In their Portland, Oregon, facility, Wavy Wood Works makes several types of wood bowls from coastal driftwood. To make a bowl, the first step is to clean the driftwood. Each piece of driftwood makes a single bowl. There is one cleaning machine. It takes 40 seconds to load each piece of wood, and the machine can hold up to 35 pieces. Once all of the pieces are loaded into the machine, it takes 45 minutes to clean the set (no matter the number of pieces in the set). Once the wood is cleaned, 15 skilled artisans carve the bowls; each one takes, on average, 100 minutes to produce each bowl. After carving, bowls are finished with a stain. It takes 30 seconds to load each bowl into the stain machine. The staining machine holds up to 35 bowls. Once all of the bowls are loaded, they are soaked for 80 minutes. After staining, bowls are unloaded onto drying racks. There is plenty of space on the drying racks. 

a. What is the maximum capacity (bowls per hour) of this process? 

b. Suppose Wavy wants to operate with the same number of bowls in each batch that are cleaned or stained. For example, if it cleans in batches of 30, then it stains in batches of 30 as well. What batch size (in bowls) minimizes its inventory while allowing the process to produce at the maximum flow rate?