C&A Pottery makes ceramic vases using a process that involves forming, drying, firing, and glazing. The $5$ workers each take an average of $60$ minutes to form a vase. The vases will then be loaded into an oven to dry. The oven can hold up to $100$ pieces; it takes $5$ minutes to load each vase. Once all the vases are loaded into the oven, it takes $24$ hours to dry each load. The dried vases are then placed in a kiln that holds up to $100$ pieces. It takes $6$ minutes to load each vase and the vases will be fired in the kiln for $72$ hours. After firing, $3$ workers each take an average of $2$ hours to glaze each vase. C&A receives an order of $1$ vase per hour. What is the smallest batch size to ensure the process is demand$-$constrained?