Consider three households (i = 1, 2, 3) each with preferences ui(xi , G) = xi × G where xi is the consumption level of private goods by household i and G is the level of public good. Private good costs 1 and public good costs 10. Individuals have income w1 = 30, w2 = 50 and w3 = 20. Determine the level of G that maximizes total welfare. (Hint: solve the problem of maximizing the sum of household utilities subject to the resource constraint.)