What is the optimal weekly purchase quantity for the chocolate croissant? What is average inventory?
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You run a food bar in UCLA Ackerman, and you sell chocolate croissants for breakfast. Your daily demand for chocolate croissants is on average 50, with a standard deviation of 8. The unit cost of a croissant is $0.70, and you sell at a unit price of $3.00. The refrigerated chocolate croissant must be consumed within 7days (one week) after purchased from your supplier, so you dispose leftover inventory and purchase fresh croissants once every week. Assume the demand in each of the seven days is independently distributed. (The z-table for
(a) What is the optimal weekly purchase quantity for the chocolate croissant? What is average inventory?
A student leader, Mark, came to you one day and told you that Anderson School would hold a special event next Thursday morning, and there would be additional demand for the chocolate croissant on that day. Mark wants to reserve a certain amount of croissant from you and sell in the special event at the regular price. You decide to give him a discounted price of $2.00. Since the croissants won’t be refrigerated in that event, any leftovers have to be disposed. Because Mark is an MBA, he decides on the reserved quantity according to the Newsvendor model.
(b) If you want to maximize the total expected profit that would be obtained by you and Mark, what should be your buyback price for the leftovers given your discounted selling price of $2.00?
(c) What is your expected profit given all the parameters in part b? (hint: use Loss function).
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- A small firm uses 3,400 lbs of chemical dye a year. Currently the firm purchases 300 lbs per order and pays $3 per order. The supplier has just announced that orders of 1,000 lbs or more will be filled at a price of $2per lb. The firm incurs a cost of $100 each time it submits an order and assigns an annual holding cost of 17% of the purchase price. If the supplier offered the discount at 1,500 lbs instead of 1,000 lbs, what order size would minimize total cost. What is the total cost at 1500A firm faces a demand of 40,000 units per month for one of its lines of stock. The firm’s cost of holding stock is £2 per unit of average stock per month, and it costs the firm a total of £100 every time it orders and acquires a new shipment of stock. The firm is willing to face stock-outs and the cost of such is £6 per unit of average stock-out per month. Assuming the firm attempts to minimise overall inventory-related costs, how large (approximately) will the firm allow its stock-outs to become before each new stock delivery arrives? A. 782 units B. 577 units C. 904 units D. 981 units * Explain in full detailSemicon is a start-up company that produces semiconductors for a variety ofapplications. The process of burning in the circuits requires large amounts ofnitric acid, which has a shelf life of only three months. Semicon estimates that itwill need between 1,000 and 3,000 gallons of acid for the next three-monthperiod and assumes that all values in this interval are equally likely. The acidcosts them $150 per gallon. The company assumes a 30 percent annual interestrate for the money it has invested in inventory, and the acid costs the company $35a gallon to store. (Assume that all inventory costs are attached to the end of thethree-month period.) Acid that is left over at the end of the three-month periodcosts $75 per gallon to dispose of. If the company runs out of acid during thethree-month period, it can purchase emergency supplies quickly at a price of$600 per gallon.a. How many gallons of nitric acid should Semicon purchase? Experience with themarketplace later shows that the demand…
- Please do not give solution in image formate thanku. You are starting a Christmas tree business. You can purchase trees from local farmers at $25 per tree. You are able to sell the trees at $75 per tree. Any leftover trees can be sold to the local wood chip company at $5 per tree. Assume that the demand follows a uniform distribution ∼U(96,380). How many trees should you stock through the holiday season?Please do not give solution in image format thanku Deltic sells this component for 55 per unit with a 4-month delivery lead time. Assume Deltic covers all transportation and related processing until delivery. TCX’s demand forecast for the upcoming selling season (12 months) is a normal distribution with mean 13500 and standard deviation 3736,4 . TCX sells each unit, after integrating their proprietary software, for 135. Assume that TCX uses a holding cost rate of 25 %, and any leftover units can be sold for 30 on average. Due to the long lead time and high minimum order quantity required, TCX is planning on a single order from Deltic to meet their needs in the next year. How many of these components should TCX order? Calculate the resulting expected annual profits for TCX.Inventory can be very expensive for firms to hold and manage. One measure of how effective a firm is at managing their inventory is the inventory sales ratio (inventory/sales). Assume a firm has quarterly sales of 1 million and inventory is normally distributed with a mean of $500k and a standard deviation of $100k. simulate the expected inventory to sales ratio for 10,000 iterations. What is the expected mean inventory to sales ratio? What is the probability that the inventory sales ratio is less than 0.5?
- You are a newsvendor selling the New York Times every morning. Before you get to work, you buy the day’s newspaper for $0.90 a copy. You sell a copy of the New York Times for $4.0. Daily demand is distributed normally with a mean of 130 and a standard deviation of 20. At the end of each morning, any leftover copies can be sold to a recycling center for $0.10. How many copies of the New YorkDemand 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?A firm that sells 5,000 blivets per month is trying to determine how many blivets to keep in inventory. The financial manager has determined that it costs $200 to place an order.The cost of holding inventory is 4 cents per month per average blivet in inventory. A five-day lead time is required for delivery of goods ordered. (This lead time is known with certainty.) The operating days per year is 250. What is the economic order quantity? What is the reorder point? At the EOQ level, what is the total carrying cost per month? At the EOQ level, what is the total ordering cost per month?