DSE 2009 Question 47: Budget constraint and consumer equilibrium

Setup, from Q46 of the paper:

A typical graduate student lives in a two-good world, books ($x$) and movies ($y$), with utility $u(x,y)=x^{1/3}y^{4/3}$. Prices of books and movies are 50 and 10. Scheme 1: 750 is paid as fellowship and an additional 250 as a book grant (the grant can only be spent on books). Assuming goods are perfectly divisible, the optimal consumption bundle under Scheme 1 is

(Same student, $u=x^{1/3}y^{4/3}$, prices 50 and 10.) Scheme 2: 1000 as scholarship and one movie free for each book purchased. The optimal consumption bundle under Scheme 2 is