The manufacturer of a product (p) currently controls 20% of the market in a particular country, while the rival brand (q) controls the rest of the market. data from previous year show that 75% of p’s customers remained loyal, while 25% switched to the rival brand. in addition, 50% of the competition’s customers did not switch to p during the year while the other 50% did. (a) respresenting the market share of each brank as a vector (whose components are fractions), formulate the problem of determining the market share next year, given the market share this year, as a matrix-vector problem (b) use the eigenvalues and eigenvectors of the matrix in (a) or any other method to determine the market share of the two products in the long run