A 68-year-old man with COPD (FEV₁ 35% predicted) presents with a 3-day history of cough, purulent sputum, and dyspnea. He was hospitalized 2 weeks ago for an acute exacerbation and discharged on oral corticosteroids. On examination: temperature 38.5°C, respiratory rate 28/min, SpO₂ 88% on room air. Chest X-ray shows a new infiltrate in the right lower lobe. Blood cultures are pending. Sputum Gram stain shows gram-negative rods. Which organism is most likely responsible, and what is the most appropriate empiric antibiotic regimen?