The Transition Matrix for Customer Purchases of Alkaline Batteries Is

question 27

Essay

The transition matrix for customer purchases of alkaline batteries is believed to be as follows: $\begin{array} { c c c c c } &{ \text { Next Purchase } } \\&\text { Duracell } & \text { Eveready } & \text { Other } \\\text { Current } \text { Duracell } & .43 & .35 & .22 \\\text { Purchase Eveready } & .38 & .45 & .17 \\\text { Other } & .13 & .25 & .62\end{array}$
A.Based on this transition matrix, what is Duracell's market share for the alkaline battery market?
B.Each 1% of the market share of the alkaline battery market is worth $3.2 million in profit.Suppose that Duracell is contemplating an advertising campaign which it believes will result in the transition probabilities for battery purchases to be as follows:
$\begin{array} { c c c c c } &{ \text { Next Purchase } } \\&\text { Duracell } & \text { Eveready } & \text { Other } \\\text { Current } \text { Duracell } & .47 & .31 & .22 \\\text { Purchase Eveready } & .38 & .40 & .22 \\\text { Other } & .22 & .25 & .53\end{array}$

What is the most that Duracell should be willing to pay for this
campaign?

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Definitions:

Arthur Conan Doyle

A British writer renowned for his detective fiction featuring the character Sherlock Holmes.

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An official record book kept by the ship's officer, detailing the ship's course, speed, distance traveled, and significant events during the voyage.

Parallel Structure

The use of consistent grammatical form within a list or series of sentences to improve clarity and flow.

Sentence Variety

Sentence variety involves using different types and structures of sentences in writing to create a more interesting and engaging narrative or argument.