Assume you are managing the company producing 2 different goods, for certainly, X and Y. Undertaken market research segmented the customer population into 5 different groups. Each group is identified by specific preference over the bundles of goods consisting of X and Y. Preferences of representative consumers from customer segment I (i=1,2,3,4,5) is described by utility function Ui(x,y), x>=0, y>=0. The utility functions Ui(x,y), (i=1,2,3,4,5) looks as follows:

U1(x,y) = (10x+4y)^0,5

U2(x,y) = -6/((2x^0,75)*(y^0,25))

U3(x,y) =0,5e^(5x+2y)

U4(x,y) = 4(5x+2y)^2

U5(x,y) = 2(x^0,75)(y^0,25)

Your company is a price-taker for both products and provides goods in any amounts demanded by the consumers for given market prices. The price for X is 12, and the price for Y equals 4. Assume that for each segment the firm is aware of the number of consumers Ni and average disposable income Mi representative the consumers type I can spend for purchasing the goods X and Y. The please get done the following assignments and explain the way you do it.

1.Determine the structure of the optimal consumption bundle under given prices for X and Y for each type of representative consumer.

2.2 - If disposable incomes are given by M1 = 360, M2 = 180, M3 = 400, M4=420, M5=540, then what amount of good x and good y will be purchased by each representative consumer i when Px=12, Py=4

3.3 - Under given prices of goods and disposable incomes of representative consumers Mi (i=1,2,3,4,5), the size of the consumers' segment is given by the number of consumers of each type N1=3000, N2=4800, N3=4000, N4=2000, N5=1200. The calculate total quantities of good x and good y that will be supplied by your company to the market.

Please be as explanatory as possible. Provide formulas and short theory explanations. Thanks!