You have been tasked to make a bridge for a mouse city that is $L=12ft$ long, the material you have selected is laminated wood and you have decided to set up the bridge on simple supports as shown in the figure. While making the bridge you realize that you need the bridge to be $8$ in$.$ tall but you do not have any wood that tall so you improvise and make the bridge out of two $3$ in beams that are glued together with a $2$ in piece of wood in the middle. If the allowable shear stress in the glued joints is $62$ psi, the allowable shear stress in the wood is $175$ psi, the allowable bending stress in the wood is $1650,$ and you apply a force $P$ a distance of $\frac{L}{3}$ from the left support, what is the max force $P$ can be$?$ You must take into consideration the self$-$weight of the wood, which is $35l\frac{b}{f}{t}^3$ peh sity

the answer is between $1\mathrm{.}5$ and $2\mathrm{.}15$