Problem 1 (Single-Period Inventory Model) (3 points) Sally's Silk Screening produces specialty T-shirts that are primarily sold at special events such as conventions and internet conferences. She is trying to decide how many to produce for an upcoming trade show due to the exact demand is unknown. For any unsold T-shirts at the end of the event, she plans to make clearance sales to empty the inventory. Sally provides below data information: It costs her $10 to produce each T-shirt, which is then sold at $20 per piece during the event. However, when the event ends, any unsold T-shirts will be sold for $4 each piece instead After collecting data over a few years, she had found that, on average, 550 T-shirts were sold at the trade show with a standard deviation of 185 T-shirts. Based on the above information, you are asked to help Sally determine the optimal quantity of T-shirts she should produce for selling at the trade show. Note: The calculation process is required to support your recommended production quantity