Consumers can choose between three cell carriers: AT&T, T-mobile, and Verizon. Aggressive marketing by all three companies results in a continual shift of customers among the three carriers. Each year,
- 50% of AT&T customers switch to T-mobile, 20% switch to Verizon, and 30% remain with AT&T.
- 40% of T-mobile customers switch to AT&T, 30% switch to Verizon, and 30% remain with T-mobile.
- 20% of Verizon customers switch to AT&T, 20% switch to T-mobile, and 60% remain with Verizon.
Currently there are 200 million AT&T customers, 100 million T-mobile customers, and 100 million Verizon users.
(a) Set up a matrix-vector product to determine how many customers (measured in millions) AT&T, T-mobile, and Verizon will each have one year from now using the information provided above.
(b) Calculate the matrix-vector product you set up in part (a) and determine the number (measured in millions) of AT&T, T-mobile, and Verizon customers one year from now.
