  We consider Prandtl's 1933 model for calculating circulation distribution
function $\Gamma$ of a finite wing which minimizes induced drag, under the
constraints of prescribed total lift and moment of inertia. We prove existence
of a global minimizer of the problem without the restriction of nonnegativity
$\Gamma\geq 0$ in an appropriate function space. We also consider an improved
model, where the prescribed moment of inertia takes into account the bending
moment due to the weight of the wing itself, which leads to a more efficient
solution than Prandtl's 1933 result.
