  In this paper we investigate upper and lower bounds of two shape functionals
involving the maximum of the torsion function. More precisely, we consider
$T(\Omega)/(M(\Omega)|\Omega|)$ and $M(\Omega)\lambda_1(\Omega) $, where
$\Omega$ is a bounded open set of $\mathbb{R}^d$ with finite Lebesgue measure
$|\Omega|$, $M(\Omega)$ denotes the maximum of the torsion function,
$T(\Omega)$ the torsion, and $\lambda_1(\Omega)$ the first Dirichlet
eigenvalue. Particular attention is devoted to the subclass of convex sets.
