A uniform load with intensity q$=22$kN$/$m acts on the entire beam, and a concentrated load P$=50$kN acts $2\mathrm{.}5$m away from the left support point. The uniform distribution load q also includes the weight of the beam. The beam is made by bonding multiple layers of wooden boards and has a cross section with a width b$=220$mm and a height h$=700$mm$.$

a$)$ Find the maximum tensile and compressive stress in the beam due to the bend.

b$)$ Find the maximum allowable load value, P$,$ if the load q remains unchanged and the allowable vertical stress at tension and compression is $1875$ psi.