Bill gets utility (satisfaction) from two goods, x and y, according to the utility function u(x,y) = ln(x) +ln(y). While Bill would like to consume as much as possible he is limited by his income, which is 100 dollars. Good x costs $2 per unit and good y costs $4 per unit, so his budget constraint is 100 = 2x + 4y. maximize Bill's utility subject to the budget constraint using the Lagrangean method.