Sarah Patel owns a boutique store that specializes in hand-made clay pottery. The annual demand for a popular vase is 700, and Sarah makes them in batches. On average, she can make 12 pots per day, and customer demand has been around 2 vases per day during the production period. The cost to set up the pottery process is $30, and it costs Sarah $3.50 to carry one vase for one year. How many vases should Sarah make in each batch to optimize her production process? If the cost to hold a vase increases to $5, what would be the batch size