Select the lightest $"4$ x $"$ beam to support a uniformly distributed load over the whole length of the simply supported beam. The live load is $12\mathrm{.}4$ lb$/$ft and the dead load is $10\mathrm{.}5$ lb$/$ft$.$ The beam is made of Southern Pine and the span is $22$ ft$.$ Deflection is not to exceed span$/240$ for the live load. Bearing length is $0\mathrm{.}5$ in$.$ at each end and the width of the beam is $3\mathrm{.}5$ in$.$ Use the method described in the textbook and videos and check for bending moment including self$-$weight, deflection, shear, and bearing.