The beam has a rectangular cross section $4$ in wide by $12$ in deep and a span of $12$ ft $.$ It is subjected to a

uniformly distributed load of $100l\frac{b}{f}t$ and concentrated loads of $600$ lb and $1200$ lb at $2$ and $7$ ft respectively,

from the left support. Assuming elastic action, determine the maximum stress at the center of the span.