Topgun Records and several movie studios have decided to sign a revenue-sharing contract for CDs. Each CD costs the studio $2 to produce. The CD will be sold to Topgun for $3. Topgun, in turn, prices a CD at $15 and forecasts demand to be normally distributed, with a mean of 5,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $1, and all sell at this price. Topgun will share 35 percent of the revenue with the studio, keeping 65 percent for itself. How many CDs should Topgun order? How many CDs does Topgun expect to sell at a discount? What is the profit that Topgun expects to make? What is the profit that the studio expects to make? Repeat parts (a)–(d) if the studio sells the CD for $2 (instead of $3) but gets 43 percent of revenue.
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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.Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.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.
- A new edition of a very popular textbook will be published a year from now. The publisher currently has 1000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution in the file P10_31.xlsx. A production run incurs a fixed cost of 15,000 plus a variable cost of 20 per book printed. Books are sold for 190 per book. Any demand that cannot be met incurs a penalty cost of 30 per book, due to loss of goodwill. Up to 1000 of any leftover books can be sold to Barnes and Noble for 45 per book. The publisher is interested in maximizing expected profit. The following print-run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with remaining sales of the current edition will be between what two values?A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.When Apple introduced its mobile payment system in 2014, the company was looking to leverage the popularity of its iPhone by adding more functionality and convenience for millions of customers. With Apple Pay, iPhone owners and Apple Watch wearers first enter their credit- or debit-card information, which Apple confirms with the banks. Once this information is on file, Apple creates a digital token that will be electronically transmitted to the retailer when an iPhone owner pays for something. To complete a purchase, the customer simply waves the phone or taps it at the checkout, uses the iPhones Touch or Face ID security to activate Apple Pay, and the phone instantly transfers the token as payment. Even though Apple Pay offers consumers the benefits of convenience and security, Apple knew it wouldnt succeed without a large network of retailers, restaurants, and other businesses agreeing to accept its mobile payments. Among the earliest businesses to sign up with Apple was McDonalds, which agreed to honor Apple Pay in its 14,000 U.S. restaurants and drive-through locations. We serve 27 million customers every day. This is a clear and compelling business opportunity for us, explained McDonalds chief information officer. Compared with cash transactions, Apple Pay transactions cost McDonalds a few pennies more to process because of bank fees. Yet the fast-food giant was willing to sign on because it saw competitive advantage and profit potential in wooing iPhone users interested in speedy checkout. Another early business supporter was Walgreens, the nationwide drug-store chain with 85 million customers enrolled in its frequent-buyer rewards program. Walgreens sells snacks, household products, and health and beauty items in addition to health-care products. Not only did Walgreens agree to accept Apple Pay at its checkout counters, but it was also the first U.S. retailer to add its rewards program to Apple Pays easy sign-on system. As a result, Walgreens customers tap twice at the checkout, once to activate the rewards account and display their savings, the second time to process the actual payment. By deciding to honor Apple Pay, Walgreens said it was enabling a simple and convenient customer experience. Several hundred thousand businesses had signed on to participate by the time Apple Pay launched in October 2014. Apples ongoing efforts to increase business participation paid off: Eighteen months later, the network of participating businesses topped 2 million, and major companies like Starbucks, Dominos, and Crate Barrel were preparing to participate. Eyeing international expansion, Apple also initiated talks with banks in China to bring Apple Pay to millions of iPhone users there. Today, Apple Pay is accepted at more than 50 percent of all U.S. retail locations and in many retail stores in twenty countries. Even though more consumers are making more mobile payments year after year, not every U.S. retailer is willing or able to work with Apple Pay. Some arent satisfied with the amount of consumer information that Apple Pay shares with participating merchants. Others would have to upgrade to new checkout technology for Apple Pay. Still others are locked into exclusive mobile payment deals with competing services. Today, mobile payments represent a small fraction of all purchase transactions, dwarfed by cash as well as by credit and debit payments. And Apple Pay faces strong competition from Google, Samsung, and others operating in the mobile-payment market. To remain a leader, Apple will have to keep signing more participating businesses and showing consumers the benefits of paying by iPhone or Apple Watch whenever they make a purchase. Which of the four categories of business markets is Apple Pay best suited for, and why?
