= Solution
The optimum axial-stiffness arrangement has continuous straight fibres parallel to the beam axis with good fibre–matrix bonding. For a common axial <strain> $\varepsilon$, <force> balance on a section gives $F=E_f\varepsilon A_f+E_m\varepsilon A_m$. Divide by total <area> and by $\varepsilon$ to obtain the <longitudinal rule of mixtures>,
$$
\boxed{E_c=V_fE_f+(1-V_f)E_m.}
$$
This is an isostrain upper idealization, consistent with the <Voigt elastic approximation>. The <glass> fraction required by the deflection constraint is
$$
V_f\ge\frac{E_{\rm req}-E_m}{E_f-E_m}=\frac{71.94-3}{75-3}=\boxed{0.9575.}
$$
\b[About 95.8% <glass> by <volume> is impractical for an ordinary glass-fibre/<polymer> board.] It leaves little matrix for wetting, load transfer and defect tolerance. Identical circular parallel fibres pack at most $\pi/(2\sqrt3)=0.9069$ in a regular hexagonal array; even that zero-void ideal gives only $68.3\,\mathrm{GPa}$. Polydisperse or noncircular fibres can change that geometric limit, so it is not an absolute theorem about every possible composite. Waviness, voids, incomplete bonding and nonaxial fibres further reduce the achievable modulus. A thicker section or a stiffer reinforcement is a more plausible design change.
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