Assume a consumer's level of satisfaction $($U$)$ when consuming units of two products, X and Y$,$ is

U$=2$x$0,6$y$04,$ where X and Y are the quantities of goods X and Y$.$ Assume furthermore that the prices

of X and Y are $$2$ and $$4$ respectively.

$1.$a Find the quantities of X and Y by making use of Lagrange if the consumer plans to consume

the products in such a way as to receive a total satisfaction of $100(1,75$ points$)$

$1.$b Calculate the budget that must be spent to acquire the combinations found in part a $(0\mathrm{.}25$

points$)$

$2.$a What would be the quantities of X and Y that this consumer should purchase if he spends a

budget of $1002(1\mathrm{.}75$ points$)$

$2.$b What would be the consumer's satisfaction from the combination found in $2.$b