A manufacturer of small garden tools has introduced a new product, a battery powered shrub/hedge trimmer. The anticipated demand is normally distributed with a mean of μ = 100 and a standard deviation of σ = 50. Each unit costs $75 to manufacture and the introductory price is to be $125. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $25 each. It costs $10 to hold a unit in inventory for the entire season. What is the cost of overstocking? What is the cost of understocking? What is the optimal cycle service level? How many units should be manufactured for sale?
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A manufacturer of small garden tools has introduced a new product, a battery powered shrub/hedge trimmer. The anticipated demand is
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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.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?
- Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. Each unit costs $180 to manufacture, and the introductory price is $250. At this price, the anticipated demand is normally distributed, with a mean of μ = 300 and a standard deviation of σ = 60. Any unsold units at the end of the season are unlikely to be valuable and will be disposed of in a post-season sale for $50 each. How many units should Green Thumb manufacture for sale? What is the expected profit from this policy? On average, how many customers does Green Thumb expect to turn away because of stocking out? Please show workings and formula in excelA book and paper store distributes one specialized monthly magazine. When looking at the sales the last years, they have concluded that the demand for each issue of the magazine will be normally distributed with an expected sale of 250 and a standard deviation of 100. The purchase price for the magazine is $20. and the sales price is $50.The store has an agreement with a second -hand store that buys unsold magazines for $5 each. How many magazines should the store buy of each issue?Green Thumb, a manufacturer of lawn care equipment has introduced a new product. Each unit cost $150 to manufacture, and the introductory price is to be $200. At this price, the anticipated demand is normally distributed, with a mean of 100 and a standard deviation of 40. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. How many units should Green Thumb manufacture for sale? What is the cycle service level (probability of not stocking out) associated with this policy? If the holding costs increase, how does this affect the optimal number of units to manufacturer and the cycle service level? *Note you can construct a graph if you prefer
- Green Thumb, a manufacturer of lawn care equipment has introduced a new product. Each unit cost $150 to manufacture, and the introductory price is to be $200. At this price, the anticipated demand is normally distributed, with a mean of 100 and a standard deviation of 40. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $50 each. It costs $20 to hold a unit in inventory for the entire season. If the manufacturing costs decrease, how does this affect the optimal number of units to manufacture and the cycle service level? *Note you can construct a graph if you prefer. What is the expected profit from this policy? (Using excel formulas from the text) On average, how many customers does Green Thumb expect to turn away because of stocking out? (hint: computed expected number of units that are understocked).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?A warehouse manager at Mary Beth Marrs Corp. needs to simulate the demand placed on a product that does not fit standard models. The concept being measured is "demand during lead time," where both lead time and daily demand are variable. The historical record for this product, along with the cumulative distribution, appear in the table. Demand During Lead Time Cumulaive Probability Probability 120 0.01 0.01 140 0.12 0.13 160 0.35 0.48 180 0.20 0.68 200 0.04 0.72 220 0.08 0.80 240 0.20 1.00 The following random numbers have been generated: 9, 78, 40, 41, and 99. (Note: Assume the random number interval begins at 01 and ends at 00.) Based on the given probabilty distribution, for the given random number the demand during the lead time is: Random Number 9 78 40 41 99 Demand The average demand during the lead time is (enter your response as an integer). The total demand during the lead time based on the five simulations is (enter your response as an integer).
- Hotel ReservationsA hotel near the university always fills up in the evening before football games. History has shown that when the hotel is fully booked, the number of last-minute cancellations has a mean of 5 and a standard deviation of 3. The average room rate is $80. When the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer. This usually costs the hotel approximately $200 because rooms booked on such late notice are expensive. How many rooms should the hotel overbook?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.Company ABC manufactures a seasonal product with uncertain demand. The production cost of the product is $130 per unit, and the product will be sold to the customers at $160 per unit. The demand of the product during a selling season is normally distributed with mean 1000 and standard deviation 300. At the end of the selling season, any unsold quantity can be disposed of in a clearance sale for $80 per unit. In order to reach the required standard imposed by an ethical and sustainable supplier certification program, ABC must improve its corporate social responsibility (CSR) performance. ABC is considering two possible investments that enable it to meet the required standard. These investments will lead to a higher CSR level, which will result in greater market demand. Investment 1 has a lump-sum cost of $2000, and it will increase the mean and standard deviation of the demand by 100 units and 20 units, respectively. Investment 2 has a lump-sum cost of $3000, and it will increase the…