Assume you are managing the company producing two different goods, for certainty, x and y. Market research conducted by the company has allowed to segment the customer population into 5 different groups. Each group is identified by specific preference over the bundles of goods consisting of x and y. Preference of representative consumer from customer segment i (i=1,2,3,4,5) is described by respective utility function U_i(x,y), x > 0, y > 0. The utility functions U_i(x,y), (i=1,2,3,4,5) look as follows:

1. Ul(X,y) = (4x+5y)0.5; 10 2. U2(X,y = (4x +5y) 3. U3(X,y) = 0.5 e-2(mint 3'5 5 X 4. U4(X,y = (min 3 5 = 2min X 5. Us(x,y) :23 +10 3 5Group 1 Group 2 Market Group 3 Group 4 Group 5 Parameter or variable Total price of x 6 6 6 6 6 N/A1 price of y 8 8 8 8 8 N/A demand for x by representative consumer NA demand for y by representative consumer NA income M 300 400 680 580 928 N/A size of group 200 250 250 200 100 NA group demand for x group demand for y