Recall Lucy and Melvin from Problem 35.6. Lucy's utility function is 2XL+G and Melvin's utility function is XMG where G is their expenditures on the public goods they share in their apartment and where XL and XM are their 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?