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Operations ManagementPractical Management ScienceBased 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.)BuyFind*arrow_forward*

6th Edition

WINSTON + 1 other

Publisher: Cengage,

ISBN: 9781337406659

Chapter 11.4, Problem 31P

Textbook Problem

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.)

Practical Management Science

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Ch. 11.2 - If the number of competitors in Example 11.1...Ch. 11.2 - In Example 11.1, the possible profits vary from...Ch. 11.2 - Referring to Example 11.1, if the average bid for...Ch. 11.2 - See how sensitive the results in Example 11.2 are...Ch. 11.2 - In Example 11.2, the gamma distribution was used...Ch. 11.2 - In Example 11.3, we commented on the 95th...Ch. 11.2 - In Example 11.3, suppose you want to run five...Ch. 11.2 - In Example 11.3, if a batch fails to pass...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...Ch. 11.3 - Rerun the new car simulation from Example 11.4,...

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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