Urgent: Operation Research- Inventory Model

Please solve step by step

Chairish-Is-The-Word, Inc., manufactures top-end hardwood chairs that are sold through a variety of retail outlets. The most popular model sells (wholesale) for $400 per chair and costs $300 to make. Past data show that average monthly demand is 1,000 chairs with a standard deviation of 200 chairs and that the normal distribution is a reasonable fit. CITW uses a 20 percent annual interest charge to estimate inventory carrying costs, so that the cost to carry one chair in stock for 1 month is $300(0.207/12 = $5. (a) If all orders are backlogged and the cost of lost customer goodwill from carrying a single chair on backorder is $20, what order-up-to (base stock) level should CITW use? (b) If any order not filled from stock is lost (i.e., the customer buys it from the competition), what order-up-to level should CITW use? (c) Explain the reason for the difference between your answers in parts (a) and (b)