Chapter 4, Problem 39RE

OHaganBooks.com has two main competitors—JungleBooks.com and FarmerBooks.com—and no other competitors of any significance on the horizon. Exercises 39–42 are based on the following table, which shows the movement of customers during July.⁴² (Thus, for instance, the first row tells us that 80% of OHaganBooks.com’s customers remained loyal, 10% of them went to JungleBooks.com, and the remaining 10% went to FarmerBooks.com.)

$\begin{array}{l}ToToTo\\ OHaganJungleFarmer\\ \begin{array}{c}FromOHagan\\ FromJungle\\ FromFarmer\end{array}\left[\begin{array}{ccc}0.8& 0.1& 0.1\\ 0.4& 0.6& 0\\ 0.2& 0& 0.8\end{array}\right]\end{array}$

At the beginning of July, OHaganBooks.com had an estimated 2,000 customers, while its two competitors had 4,000 each.

Competition Set up the July 1 customer numbers in a row matrix, and use matrix arithmetic to estimate the number of customers each company has at the end of July.