Help please

Problem 1 (Single-Period Inventory Model) (3 points) Sallys 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.

Problem 2 (Multi-Period Inventory- EOQ Model) (3 points) Gentle Bens Bar and Restaurant uses 6000-quart bottles of imported wine each year. The effervescent wine costs $4 per bottle and is served only in whole bottles because it loses its bubbles quickly. Gentle Ben figures that the ordering costs are $10 per order, and holding costs are 20% of the value of the wine (i.e., 20% of the wine cost per bottle) What is your recommended Economic Order Quantity for Gentle Ben to order (so that the total annual costs, including ordering and inventory holding costs, are minimized)? Note: The calculation process is required to support your recommended quantity. Problem 3 (Demand Variation & Safety Stock) (4 points) Healthy Hospital needs to order pairs of rubber gloves. In the past 10 days, they have experienced the following demand, which varies on a daily basis. Day Demand 1 1200 2 1000 3 800 4 900 5 1400 6 1100 7 1100 8 700 9 1000 10 800 Assume the lead time is one day and that the hospital wants a 95% service level. Then you can proceed to calculate the following: a) Average demand during lead time b) Appropriate safety stock for Healthy Hospital to hold c) The reorder point (stock quantity in inventory that would trigger the order)