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A wooden beam $(1)$ is reinforced with steel plates $(2)$ rigidly attached to its top and bottom surfaces, as shown in the figure.

Dimensions of the cross section are $b_1=6\mathrm{.}50in.,d_1=10\mathrm{.}75in.,b_2=4\mathrm{.}25in.,$ and $d_2=0\mathrm{.}50in.$ The elastic moduli of the wood

and steel are $E_1=1,250$ksi and $E_2=30,000$ksi, respectively. The allowable bending stresses of the wood and steel are $850$

and $17000$ psi, respectively. Determine the largest concentrated vertical load that can be applied at midspan if a simply supported

beam with this cross section spans $18\mathrm{.}0ft.$

$P=$