$8)(10$ points$)$ Consider the stacked blocks shown below. The upper block has a weight of $30$ lb and the lower block has a weight of $100$ lb $.$ The upper block is restrained from sliding by a cable $"$AB$".$ The coefficients of static friction are given by; $\backslash (\backslash$mu$\_\{1\}=0\mathrm{.}5\backslash )$ between the blocks and $\backslash (\backslash$mu$\_\{2\}=0\mathrm{.}25\backslash )$ between the lower block and the floor.

Determine the horizontal force $"$P$"$ required to just initiate motion of the lower block.