By ligating the b globin gene into a plasmid vector and using it to transform E. coli, both problems are solved.  First, the entire human genome is cut into 75,000 DNA fragments by a restriction endonuclease, and these are ligated into plasmids, forming a genomic library.  These are used to transform E. coli, which then reproduce to form colonies, 1 of every 750,000 carrying the b globin gene.  Second, once the colony carrying the plasmid has been isolated, the cells are placed in a continuous culture and b globin protein extracted and purified.