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 (pic 1: utility functions):

\fMarket Group 1 Group 2 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 N/A demand for y by representative consumer N/A income M 300 400 680 580 928 N/A size of group 200 250 250 200 100 N/A group demand for x group demand for y