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 39 seconds to load each piece of wood, and the machine can hold up to 36 pieces. Once all of the pieces are loaded into the machine, it takes 40 minutes to clean the set (no matter the number of pieces in the set). Once the wood is cleaned, 13 skilled artisans carve the bowls; each one takes, on average, 104 minutes to produce each bowl. After carving, bowls are finished with a stain. It takes 29 seconds to load each bowl into the stain machine. The staining machine holds up to 37 bowls. Once all of the bowls are loaded, they are soaked for 83 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.