Max has a utility function U$($x$,$ y$)=2$xy $+1.$ The prices of x and y are both $$1$ and Max has an income of $$20.$ a$.$ How much of each good will he demand? b$.$ A tax is placed on x so that x now costs Max $$2$ while his income and the price of y stay the same. How much of good x does he now demand? c$.$ Would Max be as well off as he was before the tax if when the tax was imposed, his income rose by an amount equal to $$1$ times the answer to part $($b$)?$