13. a) Pine Hill Dairy sells milk packs at different prices in Barbados (at price p) and in Antigua and Barbuda (at price q). The price of a pack of milk in Barbados is: p = 20 and in Antigua and Barbuda the price is: q = 30. Pine Hill's joint cost function for producing the milk is: C(x, y) = 2x - 4xy + 3y. (i). (ii). The government restricted the company to a total production of 26 per day due to its environmental impact. Find the number of milk packs Pine Hill should sell in each country to maximize profit subject to this government constraint. Comment on the effect of government's restriction on the production levels. (iii). Find the number of milk packs Pine Hill should sell in Barbados and Antigua and Barbuda to maximize profit. ] (ii). [1 2 -4J Find the two eigenvalues of matrix F Hence, compute the corresponding eigenvectors. b) Given the matrix: F