Lucy's utility function is 2X L +G and Melvin's utility function is X M G where G is their expenditures on the public goods they share in their apartment and where XL and X M are t heir respective private consumption expenditures. The total amount they have to spend on private goods and public goods is 36,000. They agree on a Pareto optimal pattern of expenditures in which the amount that is spent on Lucy's private consumption is 6,000. How much do they spent on public goods?