At present, a fraction π1 = ⅔ of all purchases are cola 1 purchases, since:
π1 = .90π1+.20π2 π2 = .10π1+.80π2
and using the following equation by π1 + π2 = 1
Each purchase of cola 1 earns the company a $1 profit. We can calculate the annual profit as $3,466,666,667 [2/3(100 million)(52 weeks)$1].
The advertising firm is offering to change the P matrix to