Chapter 9, Problem 39RE

Marketing. Recent technological advances have led to the development of three new milling machines: brand $A$, brand $B$, and brand $C$. Due to the extensive retooling and startup costs, once a company converts its machine shop to one of these new machines, it never switches to another brand. Each year, $6\%$ of the machine shops convert to brand $A$ machines. $8\%$ convert to brand $B$ machines, $11\%$ convert to brand $C$ machines, and the remainder continue to use their old machines.

(A) In the long run, what is the market share of each brand?

(B) What is the average number of years that a company waits before converting to one of the new milling machines?