$1$ Suppose $we$ have a consumer with utility $U(x,Y)=x^{\frac{2}{5}}{Y}^{\frac{3}{5}}.$ She has income $M=$$$200$ and faces

prices $Px=$$$4$ and $Py=$$$5.$

Clearly state the Consumer's Optimization $(choice)$ Problem $in$ words.

Sketch the problem $(budget$ set, indifference curves, and optimal solution$)$

What two equations describe the solution $to$ the problem. Explain.

Solve for optimal consumption $x^{*}$ and $Y^{*}.$