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Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let p A denote the probability that a gallon produced by company A is of unsatisfactory quality, and define p B and p C similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B /( B + C ) that he will switch to brand B and probability C /( B + C ) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume p A = 0.10 , p B = 0.15, and p C = 0.20. ( Hint : You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV ( ntrials, psuccess , RAND()).) b. Suppose a 1% increase in market share is worth $10,000 per week to company A. Company A believes that for a cost of $1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of p A , p B , and p C as in part a.)

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

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BuyFindarrow_forward

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 11.4, Problem 31P
Textbook Problem
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Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands.

  1. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).)
  2. b. Suppose a 1% increase in market share is worth $10,000 per week to company A. Company A believes that for a cost of $1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)

a)

Summary Introduction

To determine: The market share for each firm after a year.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Formulae to determine the above table:

b)

Summary Introduction

To determine: Whether the given change is worthwhile.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

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Chapter 11 Solutions

Practical Management Science
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Ch. 11.3 - In the cash balance model from Example 11.5, the...Ch. 11.3 - In the cash balance model from Example 11.5, is...Ch. 11.3 - Run the retirement model from Example 11.6 with a...Ch. 11.3 - The simulation output from Example 11.6 indicates...Ch. 11.3 - Modify the model from Example 11.6 so that you use...Ch. 11.3 - Referring to the retirement example in Example...Ch. 11.3 - A European put option allows an investor to sell a...Ch. 11.3 - Modify Example 11.8 so that the portfolio now...Ch. 11.3 - Change the new car simulation from Example 11.4 as...Ch. 11.3 - Based on Kelly (1956). You currently have 100....Ch. 11.3 - Amanda has 30 years to save for her retirement. At...Ch. 11.3 - In the financial world, there are many types of...Ch. 11.3 - Suppose you currently have a portfolio of three...Ch. 11.3 - If you own a stock, buying a put option on the...Ch. 11.3 - For the data in the previous problem, the...Ch. 11.3 - A stock currently sells for 69. The annual growth...Ch. 11.3 - A knockout call option loses all value at the...Ch. 11.3 - Suppose an investor has the opportunity to buy the...Ch. 11.4 - Suppose that Coke and Pepsi are fighting for the...Ch. 11.4 - Seas Beginning sells clothing by mail order. An...Ch. 11.4 - Based on Babich (1992). Suppose that each week...Ch. 11.4 - The customer loyalty model in Example 11.9 assumes...Ch. 11.4 - We are all aware of the fierce competition by...Ch. 11.4 - Suppose that GLC earns a 2000 profit each time a...Ch. 11.4 - The Mutron Company is thinking of marketing a new...Ch. 11.5 - A martingale betting strategy works as follows....Ch. 11.5 - The game of Chuck-a-Luck is played as follows: You...Ch. 11.5 - You have 5 and your opponent has 10. You flip a...Ch. 11.5 - Assume a very good NBA team has a 70% chance of...Ch. 11.5 - Consider the following card game. The player and...Ch. 11.5 - Based on Morrison and Wheat (1984). When his team...Ch. 11 - You now have 5000. You will toss a fair coin four...Ch. 11 - You now have 10,000, all of which is invested in a...Ch. 11 - Suppose you have invested 25% of your portfolio in...Ch. 11 - A ticket from Indianapolis to Orlando on Deleast...Ch. 11 - Based on Marcus (1990). The Balboa mutual fund has...Ch. 11 - Consider a device that requires two batteries to...Ch. 11 - Appliances Unlimited (AU) sells refrigerators. Any...Ch. 11 - The annual demand for Prizdol, a prescription drug...Ch. 11 - A company is trying to determine the proper...Ch. 11 - The DC Cisco office is trying to predict the...Ch. 11 - A common decision is whether a company should buy...Ch. 11 - Suppose you begin year 1 with 5000. At the...Ch. 11 - You are considering a 10-year investment project....Ch. 11 - Play Things is developing a new Lady Gaga doll....Ch. 11 - An automobile manufacturer is considering whether...Ch. 11 - It costs a pharmaceutical company 75,000 to...Ch. 11 - Suppose you buy an electronic device that you...Ch. 11 - Rework the previous problem for a case in which...Ch. 11 - Chemcon has taken over the production of Nasacure...Ch. 11 - The Tinkan Company produces one-pound cans for the...Ch. 11 - You are unemployed, 21 years old, and searching...Ch. 11 - In this version of dice blackjack, you toss a...Ch. 11 - It is January 1 of year 0, and Lilly is...Ch. 11 - It is January 1 of year 0, and Merck is trying to...Ch. 11 - Suppose you are an HR (human resources) manager at...Ch. 11 - You are an avid basketball fan, and you would like...Ch. 11 - Suppose you are a financial analyst and your...Ch. 11 - Software development is an inherently risky and...Ch. 11 - Health care is continually in the news. Can (or...

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