In their Portland, Oregon facility, Wavy Wood Works makes serveral types of wood bowls from coastal drift wood. To make a bowl, the first step is to clean the drift wood. Each piece of drift wood make a single bowl. There is one cleaning machine. It takes 43 seconds to load each piece of wood and the machine can hold up to 37 pieces. Once all the pieces are loaded into the machine, it takes 42 minutes to clean the set (no matter the number of pieces in the set). Once the wood is cleaned, 19 skilled artisans carve the bowls, each one takes on average 94 minutes to produce each bowl. After carving, bowls are finished with a stain. It takes 25 seconds to load each bowl into the stain machine. The staining machine holds up to 30 bowls. Once all the bowls are loaded, they are soaked for 76 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? ______ bowls per hour
b. Suppose Wavy wants to operate with the same number of bowls in each batch that is cleaned or stained. For example, if they clean in batches of 30, then they stain in batches of 30 as well. What batch size (in bowls) minimizes their inventory while allowing the process to produce at the maximum flow rate? (Round to 2 decimal places). ______ bowls per batch.