$2\mathrm{.}1.$ Violet buys pies $(x)$ and champagne $(y)$ with her income of $$100.$ The price of champagne is $p_y=$$$5$ per bottle. Draw her budget constraints in each of the following cases assuming that both goods are divisible.

$($a$)$ Pies cost $p_x=$$$5$ per pie if she buys between zero and $10$ pies, and $$4$ per pie if she buys more than $10$ pies.

$($b$)$ Pies cost $p_x=$$$5$ per pie if she buy? between zero and $10$ pies; if she buys more than $10$ pies, each additional pie or $($fraction thereof$)$ is half$-$price, i$.$e$.,p_x=$$$2\mathrm{.}50.$