$6\mathrm{.}6$ In Figure P$6\mathrm{.}6$ blocks A and $B$ weigh $50$ lb and

$100$ lb $,$ respectively. The coefficients of friction are: ${}_1$

$=0\mathrm{.}2$ between A and $B,$ and ${}_2=0\mathrm{.}35$ between $B$ and the

horizontal plane. Find the smallest force $P$ that will cause

$A$ to move to the left.