Suppose that a consumer has the following utility function, u (x, y) = 3x ^ 2y ^ 3 that describes his consumption preferences. This individual wants to formulate a consumption plan for two goods x and y, whose market prices are px = 3 and py = 12, respectively. This consumer has an income of 1200 um. Determine, what is the basket of consumption x and y that this consumer will choose?

a) x = 2.66, y = 124.33

b) x = 1.64, y = 215.99

c) x = 3.66, y = 127.36

d) x = 1.66, y = 254.66

3. Consumer Adam prefers to consume goods a and y in fixed proportions of two-for-three. In other words, his utility function is U(x, y) = min(er, zy) or U(x, y) = min(3x, 2y). His income is 10. (a) Suppose the prices of goods i and y are 1 and 2, respectively. Obtain the optimal consumption bundle. (b) Suppose the prices of goods z and y are 2 and 2, respectively. Obtain the optimal consumption bundle