A 48-year-old woman with a 6-week history of nasal obstruction, postnasal drip, and recurrent episodes of purulent rhinorrhea is diagnosed with chronic rhinosinusitis unresponsive to saline irrigation and intranasal corticosteroids. Culture of sinus secretions grows *Pseudomonas aeruginosa* and *Staphylococcus aureus*. What is the drug of choice for this case?