EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 8220100460463
Author: Anderson
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 21.3, Problem 12E
Martin’s Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the station’s pick-up truck or a new heavy-duty snowplow truck. After analyzing the situation, Martin believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits/losses apply.
The probabilities for the states of nature are P(s1) = .4, P(s2) = .3, and P(s3) = .3. Suppose that Martin decides to wait until September before making a final decision. Assessments of the probabilities associated with a normal (N) or unseasonably cold (U) September are as follows:
| P(N) = .8 | P(s1 | N ) 5 .35 | P(s1 | U ) 5 .62 |
| P(U) = .2 | P(s2 | N ) 5 .30 | P(s2 | U ) 5 .31 |
| P(s3 | N ) 5 .35 | P(s3 | U ) 5 .07 |
- a. Construct a decision tree for this problem.
- b. W hat is the recommended decision if Martin does not wait until September? What is the
expected value ? - c. W hat is the expected value of perfect information?
- d. W hat is Martin’s optimal decision strategy if the decision is not made until the September weather is determined? What is the expected value of this decision strategy?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return.
Investment Opportunity
Rate of Return
Municipal Bonds (X1)
0.095
High Tech Stock (X2)
0.146
Blue Chip Stock (X3)
0.075
Federal Bonds (X4)
0.070
a) The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, at least 25 percent Blue Chip Stock, no more than 30 percent High Tech and Blue Chip Stock, and no more than 15 percent High Tech Stock.
Based on above problem, how many constraints are in this problem?
A) 3
B) 4
C) 5
D) 2
b) Based on part a, which of the…
Help me fast so that I will give Upvote.
A student has decided that passing a mathematics course will, in the long run, be
twice as valuable as passing any other kind of course. The student estimates that passing a typical math course will require 12hr a week to study and do homework. The student estimates that any other course will require only 8hr a week. The student has 48hr available for study per week. How many of each kind of course should the student take? (Hint: The profit could be viewed as 2 “value points” for passing a math course and 1 “value point” for passing any other course.) How, if at all, do the maximum value and optimal course mix change if the student decides to take at least two math courses and two other courses?
Chapter 21 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
Ch. 21.2 - Prob. 1ECh. 21.2 - A decision maker faced with four decision...Ch. 21.2 - Hudson Corporation is considering three options...Ch. 21.2 - Myrtle Air Express decided to offer direct service...Ch. 21.2 - The distance from Potsdam to larger markets and...Ch. 21.2 - Seneca Hill Winery recently purchased land for the...Ch. 21.2 - The Lake Placid Town Council has decided to build...Ch. 21.3 - Consider a variation of the PDC decision tree...Ch. 21.3 - A real estate investor has the opportunity to...Ch. 21.3 - Dante Development Corporation is considering...
Ch. 21.3 - Hales TV Productions is considering producing a...Ch. 21.3 - Martins Service Station is considering entering...Ch. 21.3 - Lawsons Department Store faces a buying decision...Ch. 21.4 - Suppose that you are given a decision situation...Ch. 21.4 - In the following profit payoff table for a...Ch. 21.4 - To save on expenses, Rona and Jerry agreed to form...Ch. 21.4 - The Gorman Manufacturing Company must decide...Ch. 21 - An investor wants to select one of seven mutual...Ch. 21 - Warren Lloyd is interested in leasing a new car...Ch. 21 - Hemmingway, Inc. is considering a 50 million...Ch. 21 - Embassy Publishing Company received a six-chapter...Ch. 21 - Lawsuit Defense Strategy John Campbell, an...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forwardFor the next three items, consider the following scenario: Chaka Furniture Shop located in Cavite makes two kinds of products, cabinets and dressers, which pass through the assembly and the finishing departments. The Assembly department has 60 hours of work available each week, while the finishing department has 48 hours each week. Making one cabinet needs 2 hours in Finishing and 4 hours in Assembly, while it takes 2 hours to assemble a dresser and 4 hours to finish it. If the profit generated per cabinet is P100 and per dresser is P80.(Hint: Let x be the number of cabinet produce and y be the number of dresser produce). 21. Which of the following LP model is the best describe from the given problem? (Ь) (c) Mаx P (a) (d) Max P = 100x + 80y Mаx P 100x + 80y 80x + 100y Маx Р = 100x + 80y %3D subject to subject to subject to subject to 2x + 4y 60 4x + 2y 48 х, у 2 0 х, у 20 х, у > 0 х, у > 0 22. How many units of cabinet should the company produce to maximize the profit? (а) 15 (b) 12…arrow_forward
- Store A and Store B compete for the business of the same customer base. Store A has 55% of the business and Store B has 45 %. Both companies intend to expand to increasse their market share. If both expand, or neither expand, they expect theri market share to remain the same. If Store A expands and Store B does not, the Store A"A share increases to 65%. If Store B expands and Store A doesnt, then Store A's share drops to 50%. Determine which strategy, to expand or not, each company should take.arrow_forwardDataware is trying to determine whether to give a $10 rebate, to cut the price $6, or to have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increas e sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%. a) Build the basic model to compute the profits of the three options. b) What increase in sales from the rebate would make the r ebate and price cut equally desirable? c) Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will incr ease sales by between 10% and 30%. Perform a sensitivity analysis that could be used to help determine Dataware ’ s course of actionarrow_forwardThe Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?arrow_forward
- The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you invest to get a return of 250 dollars in 1 year?arrow_forwardAlthough investing all at once works best when stock prices are rising, dollar-cost averaging can be a good way to take advantage of a fluctuating market. Dollar-cost averaging is an investment strategy designed to reduce volatility in which securities are purchased in fixed dollar amounts at regular intervals regardless of what direction the market is moving. This strategy is also called the constant dollar plan. You are considering a hypothetical $1,200 investment in a media company's stock. Your choice is to invest the money all at once or dollar-cost average at the rate of $100 per month for one year. Assume that the company allows you to purchase "fractional" shares of its stock. (a) If you invested all of the money in January and bought the shares for $12 each, how many shares could you buy? shares (b) From the following chart of share prices, calculate the number of shares that would be purchased each month using dollar-cost averaging and the total shares for the year.…arrow_forwardAlthough investing all at once works best when stock prices are rising, dollar-cost averaging can be a good way to take advantage of a fluctuating market. Dollar-cost averaging is an investment strategy designed to reduce volatility in which securities are purchased in fixed dollar amounts at regular intervals regardless of what direction the market is moving. This strategy is also called the constant dollar plan. You are considering a hypothetical $1,200 investment in a media company's stock. Your choice is to invest the money all at once or dollar-cost average at the rate of $100 per month for one year. Assume that the company allows you to purchase "fractional" shares of its stock. (a) If you invested all of the money in January and bought the shares for $12 each, how many shares could you buy? shares (b) From the following chart of share prices, calculate the number of shares that would be purchased each month using dollar-cost averaging and the total shares for the year. Round to…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY