Among all smooth simple closed curves in the plane, oriented counterclockwise, find the one along which work done by

$F=(\frac{1}{4}{x}^{2}y+\frac{1}{3}{y}^3)i+xj$

is greatest.

$x^2+y^2=1$

$\frac{x^2}{4}+y^2=1$

$x^2+\frac{y^2}{4}=1$

$x^2+y^2=4$