In The Winter's Tale, how does Paulita convince the king of Bohemia to let her marry his son?

In The Winter's Tale, Polixenes finds out about his son's love for Perdita. He and Camillo visit the shepherd's house in disguise. Perdita loves Forizel. Florizel asks the stranger, actually his father, to witness his marriage vow to Perdita. His father reveals his identity and reproaches Florizel for wanting to marry a low-born maid. Perdita makes a noble speech about the unimportance of wealth. Camillo is charmed by Perdita's nobility.