Solution (source code)

= Solution

Both outer faces of the <cantilever> are loaded, so use the pine's lower longitudinal <compressive strength>, $40\,\mathrm{MPa}$, rather than its $85\,\mathrm{MPa}$ <tensile strength>. Consistent SI units give $M_A$ values $(2.564,2.143,0.7273)\times10^5\,\mathrm{m^2s^{-2}}$ for steel, aluminium and pine respectively. Their $M_B$ values are $5.734,8.748,11.499\,\mathrm{Pa^{1/2}m^3kg^{-1}}$. Hence \b[Design A: steel best, pine worst; Design B: pine best, steel worst.] Aluminium is intermediate in both cases. These rankings concern the stated strength constraint; a <toughness> or deflection constraint could change feasibility.