Please answer questions 9 and 10 based on this data. Daily demand for packages of five videotapes at a warehouse store is found to be normally distributed with a mean of 50 and a standard deviation of 5. When the store orders more tapes, the orders take four days to arrive. Assume the store is open 360 days a year. If the store wants the probability of stocking out to be no more than 5%, and demand each day is independent of the day before, what should be the safety stock? Please round your answer to two decimals. Safety stock= 17 Question 10 4 pts If the store wants the probability of stocking out to be no more than 5%, and demand each day is independent of the day before, what reorder point should be set? Please round your answer to two decimals. Reorder point=
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- That One Book sells its books through The Witch and the Wardrobe bookstores. It costs That One Book $0.80 to print each book; it sells the book to The Witch and the Wardrobe for $2.50. The Witch and the Wardrobe then sells the books at retail for $6.00. Whatever doesn’t sell gets thrown away. Demand for the book each issue is normal with a mean of 5219 and a standard deviation of 1610. To give The Witch and the Wardrobe incentive to order more books, it proposes a revenue-sharing contract. Instead of selling the book to The Witch and the Wardrobe for $2.50, That One Book will sell its books to The Witch and the Wardrobe for only $1.00. However, for each book that The Witch and the Wardrobe sells at retail, The Witch and the Wardrobe must give $2.00 back to That One Book. With this revenue sharing agreement in place, what is the optimal order amount that will maximize The Witch and the Wardrobe expected profit? Please do fast ASAPis selling Christmas trees. She purchases trees for $10 and sells for $25 each. The number of trees she can sell is normally distributed with a mean of 100 and standard deviation of 30. How many trees should purchase?13 Pam’s demand for hats is normally distributed with mean 500 and standard deviation 100. She sells her hats for $50 each and buys hats for $10 each, and anything she can't sell by the end of the year, the wholesaler will buy for $5 each. How many hats should she order for next year to maximize profit?
- A newsvendor orders 8000 units. Demand is normally distributed with a mean of9000 and a standard deviation of 2000. What is the stockout probability?Dan’s Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails for $28.00. The publisher sells the book to Dan at $20.00. Dan can dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. Question 1: What is the quantity that Dan should order to maximize his expected profit?Dan's Independent Book Store is trying to decide how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $28.00. The publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is normal with a mean of 1000 and a standard deviation of 250. The publisher is thinking of offering the following scheme to Dan. At the end of the season, they will buy back unsold copies at a pre-determined price of $17.00. However, Dan would have to bear the costs of shipping unsold copies back to the publisher at $1.00 per copy. What is the quantity that Dan should order, to maximize his expected profits?
- Demand in each period is normally distributed with a mean of 100 and standard deviation of 50. Assuming demand across periods are independent, what is the standard deviation of the total demand over 4 periods?You have been asked to help a manufacturing firm that produces a variety of specialty components for local auto speed shops. The firm orders a number of components from suppliers, but the one they have asked you to analyze is special welding rod. Historical data suggests daily consumption of these rods can be modeled by a normal distribution with a mean and standard deviation of 42.3 and 5.1 bolts per day, respectively. The rods come in boxes of 5 rods/box, and the supplier will only ship in box quantities. It takes 2 days to receive an order from the supplier. You may assume that the daily demands are independent and identically distributed, and that inventory position is always known (i.e., continuous review). 1. The current policy is the order thirty boxes from the supplier when inventory position reaches ten boxes. What is the long run fraction of stock outs associated with the current strategy? 2. Assume the cost to place an order is $5 and holding is estimated to be…XYZ Company must order tires from its warehouse. It costs $10400 to place an order and to review the inventory level. Annual tire sales are normally distributed with mean 18000 and variance 4,000,000. It costs $8 per year to hold a tire in inventory, and each order arrives two weeks after being placed. The Company uses periodic review (R, S) policy. What is the review interval R (in years), estimated using EOQ.? Select one: a. 0.3801 b. 0.19 c. 0.2687 d. 1.075 e. 0.1267
- A product’s demand over (L + 1) periods follows a normal distribution withmean 1000 and standard deviation 400. The order-up-to level is 1600. What is thein-stock probability?= A small manufacturing facility stocks a single-use filter, part SUF100, for their production process. It costs the manufacturer $1.50 per filter to purchase and $100 per order placed. They use a holding cost of 28% annually. Monthly demand for SUF100 follows a normal distribution with u 280 and σ = = 77. The parts arrive five months after an order is placed. If a stockout occurs, the demand is backlogged, not lost, and costs the production facility $12.80 per part backordered. 1. Find the optimal order quantity and reorder level to minimize average annual cost of holding, setup, and stockout. 2. What is the average annual cost of holding, setup, and stockouts, when the Q,R-policy in part 1 is used?Your company currently keeps a safety stock of 554 units of a particular product that has a lead time of 10 days. Records indicate that the weekly demand was as follows: 1176 955 780 1052 736 842 748 993 852 738 794 1444 1333 1372 1106 706 923 734 786 729 1357 1165 1277 683 1106 What is the current service level? Input your result as the decimal form and round to 4 decimal places. You are requested to recommend a safety stock that will ensure an average service level of 97.5%. The lead time is not expected to change. What safety stock would you recommend? (0 decimal places)