The Transition Matrix for Customer Purchases of Alkaline Batteries Is

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?