A consumer's preferences over two goods are represented by:

U(x1, x2) = (x1^2)(x2^3)/100

The prices are P1 and P2, and an amount of money E can be spent on these goods.

a) Show that the two uncompensated demand functions are:

x1 = 2E/5p1 and x2 = 3E/5p2

b) How do you know that these demands maximise utility rather than minimising it?

c) Suppose that p1 = $4, p2 = $5 and E = $100. Use the results in a) to find the optimal quantities demanded of the tw0 goods, and the resulting amount of 'utils' obtained. Assume that both goods are divisible, so fractions are possible.