We shall now describe in turn these three basic steps$$branching$,$ bounding, and fathoming$$and illustrate them by applying a branch$-$and$-$ bound algorithm to the prototype example $($the California Manufacturing Co$.$ problem$)$ presented in Sec. $12\mathrm{.}1$ and repeated here $($with the constraints numbered for later reference$).$

Maximize subject to

and

Branching