45. A product manager at Clean & Brite (C&B) wantsto determine whether her company should market anew brand of toothpaste. If this new product succeeds in the marketplace, C&B estimates that itcould earn $1,800,000 in future profits from thesale of the new toothpaste. If this new productfails, however, the company expects that it couldlose approximately $750,000. If C&B chooses notto market this new brand, the product managerbelieves that there would be little, if any, impacton the profits earned through sales of C&B’s otherproducts. The manager has estimated that the newtoothpaste brand will succeed with probability 0.35.Before making her decision regarding this toothpaste product, the manager can spend $130,000 ona market research study. Based on similar studieswith past products, C&B believes that the studywill predict a successful product, given that productwould actually be a success, with probability 0.80.It also believes that the study will predict a failure,given that the product would actually be a failure,with probability 0.70.a. To maximize expected profit, what strategy shouldthe C&B product manager follow?b. Calculate and interpret EVI for this decision problem.c. Calculate and interpret EVPI for this decisionproblem

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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45. A product manager at Clean & Brite (C&B) wants
to determine whether her company should market a
new brand of toothpaste. If this new product succeeds in the marketplace, C&B estimates that it
could earn $1,800,000 in future profits from the
sale of the new toothpaste. If this new product
fails, however, the company expects that it could
lose approximately $750,000. If C&B chooses not
to market this new brand, the product manager
believes that there would be little, if any, impact
on the profits earned through sales of C&B’s other
products. The manager has estimated that the new
toothpaste brand will succeed with probability 0.35.
Before making her decision regarding this toothpaste product, the manager can spend $130,000 on
a market research study. Based on similar studies
with past products, C&B believes that the study
will predict a successful product, given that product
would actually be a success, with probability 0.80.
It also believes that the study will predict a failure,
given that the product would actually be a failure,
with probability 0.70.a. To maximize expected profit, what strategy should
the C&B product manager follow?
b. Calculate and interpret EVI for this decision problem.
c. Calculate and interpret EVPI for this decision
problem

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