$3\mathrm{.}12.$ A cantilever beam with four strain gages is used as a load transducer, as shown in Fig. P$3\mathrm{.}12.$ A full Wheatstone bridge is to be used. Show the positions of four gages in the

bridge so that maximum sensitivity is obtained and the output is equal to $(V{G}_{f}d\frac{h}{2}EI)P$; comment on the dimension $d$ in relation to sensitivity$.$ Note that $V$ and $G_f$ are the bridge excitation voltage and gage factor, respectively.