= Solution
With $w$ fixed, bending strength requires $h=\sqrt{6FL/(w\sigma_f)}$. Substitution into the <cantilever> <mass> gives
$$
m_B=L\sqrt{6FLw}\frac{\rho}{\sqrt{\sigma_f}}.
$$
The <material performance index> to maximize is therefore
$$
\boxed{M_B=\frac{\sqrt{\sigma_f}}{\rho}}.
$$
Changing the free geometric variable changes the strength exponent. A stiffness-limited problem would instead involve <Young's modulus>; the supplied modulus does not enter this strength-only index.
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