There are two goods in the economy, apples and bananas. The price of an apple is p = 7. The price of a banana is q = 6. The consumer has wealth equal to W = 168. Let x denote the number of apples and y denote the number of bananas. Solve the following utility maximization problems when the preferences of a consumer are characterized by the following utility functions (in each item clearly determine the budget constraint equation and the expenditures in each good): (7.a) U(x, y) = xy. (7.b) U(x, y) = x+y. (7.c) U(x, y) = 3x + 2y. = (7.d) U (x, y) = min{x,y}. (7.e) U(x, y) = min{3x, y}. (7.f) U(x, y) = min{3x, 2y}. (7.g) U(x, y) = max{x,y}.