The owner of a boat has estimated the following distribution of demand for a particular kind of boat. No. demanded o 1 2 3 Probability 0.10 0.20 0.30 0.40 Each boat costs him (c + d) rials and he sells them for (2 • c + 2 • d) rials each. Prices are given in hundreds rial units. Boats that are left unsold at the end of the season must be disposed off for (c + d – 2) rials each. How many should be stocked so as to maximize his expected profit?

The owner of a boat has estimated the following distribution of demand for a particular kind of boat. No. demanded o 1 2 3 Probability 0.10 0.20 0.30 0.40 Each boat costs him (c + d) rials and he sells them for (2 • c + 2 • d) rials each. Prices are given in hundreds rial units. Boats that are left unsold at the end of the season must be disposed off for (c + d – 2) rials each. How many should be stocked so as to maximize his expected profit?

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Description: The owner of a boat has estimated the following distribution of demand for a particular kind of boat.No. demanded o1 2 3Probability0.10 0.20 0.30 0.40Each boat costs him (c + d) rials and he sells them for (2 • c + 2 • d) rials each. Prices are give

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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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?
The annual demand for Prizdol, a prescription drug manufactured and marketed by the NuFeel Company, is normally distributed with mean 50,000 and standard deviation 12,000. Assume that demand during each of the next 10 years is an independent random number from this distribution. NuFeel needs to determine how large a Prizdol plant to build to maximize its expected profit over the next 10 years. If the company builds a plant that can produce x units of Prizdol per year, it will cost 16 for each of these x units. NuFeel will produce only the amount demanded each year, and each unit of Prizdol produced will sell for 3.70. Each unit of Prizdol produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. a. Among the capacity levels of 30,000, 35,000, 40,000, 45,000, 50,000, 55,000, and 60,000 units per year, which level maximizes expected profit? Use simulation to answer this question. b. Using the capacity from your answer to part a, NuFeel can be 95% certain that actual profit for the 10-year period will be between what two values?
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The retail price of a Mother’s Day cake in San Ramon Safeway is $30.00. A local bakery sells the cakes to the Safeway at $20.00. The Safeway will dispose of all of the unsold cakes at 50% off the retail price, at the end of the Mother’s Day weekend. The manager in Safeway estimates that demand for this cake during the Mother’s Day weekend is Normal Distribution with a mean of 100 cakes and a standard deviation of 50 cakes. (1) How many cakes should San Ramon Safeway order from the bakery? (2) If the store manager learned a new forecast method in a class that would reduce the standard deviation of estimated demand from 50 to 25 (mean remains 100), how many cakes should San Ramon Safeway order from the local bakery?