Three stone blocks rest on the ground as shown. Block B weighs $90$ lb $,$ and Block C weighs $340$ lb $.$ The coefficient of static friction between the blocks and the ground is

${}_{s_{\text{g}\text{r}\text{o}\text{u}\text{n}\text{d}}}$

$=0\mathrm{.}5,$ and the coefficient of static friction between the blocks is

${}_{s_{\text{b}\text{l}\text{o}\text{c}\text{k}\text{s}}}$

$=0\mathrm{.}3.$ Determine the minimum required weight of Block A such that Block C wedges Block B upward before the three blocks slide together. Express your answer in lb to the nearest whole lb$.$

Your written solution must include all necessary FBDs and calculations for the magnitude of the force $P$ required for Block C to wedge Block B upward and weight of Block A required to prevent sliding of the three blocks together.