What is the quantity that Dan should order to maximize his expected profit?
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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.
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What is the quantity that Dan should order to maximize his expected profit?
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- Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)
- Magdeleine James is a sole trader, who sells souvenir T-shirts. She wishes to sell her T-shirts at the Tobago Jazz festival. Each t-shirt cost $165 to produce and sells for $225. After the festival, she reduces the sale price of the T-shirts by 70% in order to sell them off. Experience from previous years has shown that the demand for these T-shirts at the festival is 82, with a standard deviation of 21. How many T-shirts should Magdeleine take to sell at the festival?A home improvement store sells boxwood shrubs during the spring planting season. Each boxwood sells for $35 and it costs the store $13 to purchase and transport each boxwood from its supplier. At the end of the season, any remaining boxwoods are sold to a local landscaper at a deep discount for $5/boxwood. In the upcoming season, demand for boxwoods is forecast to be normally distributed with a mean of 1,000 and a standard deviation of 200 (you may assume demand is continuous). If the store can only order once at the beginning of the season, how many boxwoods should be stocked?Every four years, Blockbuster Publishers revises its textbooks. It has been three years since the best-selling book, The Joy of OR, has been revised. At present, 2,000 copies of the book are in stock, and Blockbuster must determine how many copies of the book should be printed for the next year. The sales department believes that sales during the next year are governed by the distribution in Table 8. Each copy of Joy sold during the next year brings the publisher $35 in revenues. Any copies left at the end of the next year cannot be sold at full price but can be sold for $5 to Bonds Ennoble and Gitano’s bookstores. The cost of a printing of the book is $50,000 plus $15 per book printed. How many copies of Joy should be printed? Would the answer change if 4,000 copies were currently in stock? Table 8: Copies Demanded Probability 5,000 .30 6,000 .20 7,000 .40 8,000 .10
- Good Shoes Company manufactures ski boots for children each pair of which costs $40 to manufacture. Good Shoes sells the boots to a well-known sports goods retailer and the retailer sells each pair for $100. Any boots not sold (by the retailer) during the season are sold to a discount retailer for $20 a pair. Demand during the season is assumed to have a Normal distribution with a mean of 850 and a standard deviation of 350. What should the manufacturer charge the retailer per pair to maximize its expected profits? Assume that Good Shoes will consider a price from the following set: (60,65,70,75,80,85 90,95), i.e., The manufacturer's price will be either $60, or $65 or $70, or ......,,$95).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?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 retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit. All units not sold during the regular season are sold for half the retail price in an end-of-season clearance sale. Assume that demand for the product is uniformly distributed between 200 and 800. What is the recommended order quantity? What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? That is, what is the probability of a stock-out using your order quantity in part (a)? To keep customers happy and returning to the store later, the owner feels that stock-outs should be avoided if at all possible. What is your recommended order quantity if the owner is willing to tolerate a 0.15 probability of a stock-out?A grocer purchases plums for $2.95 per pound and sells them for $4.62 per pound. At the end of the sales cycle, leftover plums are sold for a closeout price of $1.76 per pound. The grocer purchases 10,380 pounds of plums. Expected demand is normally distributed with a mean of 8,304 pounds and a standard deviation of 1,038. What is the grocer's expected profit?Firewire is a high-end manufacturer of surfboards. A surfboard is sourced at a cost of $80 and sold for $125 to surf shops in its home market (United States). One order is placed at the beginning of the summer season. Currently, Firewire disposes any unsold boards to their outlet store affiliates for $70. It costs $10 to hold a board in inventory for the entire season and ship it to outlet affiliates. Demand for this item is forecasted to be normally distributed with a mean of 4,000 units and a standard deviation of 1750 units. A) Please provide ideal service level and order quantity? Expected profits? Expected overstock to outlets?.... under your preferred policy. B) If Firewire chooses instead of outlets to ship to Australia surf shops, the salvage value would increase to $75 per unit (board) including all associated costs (including the aforementioned holding costs). Would this be a better option?….please show each result as in part A for this alternative scenario to justify your…