A 68-year-old man with COPD (FEV₁ 35% predicted) presents to the emergency department with a 3-day history of productive cough, fever (38.5°C), and dyspnea. He lives in a nursing home and was hospitalized 2 weeks ago for acute exacerbation of COPD, treated with antibiotics for 5 days. On examination: respiratory rate 28/min, SpO₂ 88% on room air, crackles in the right lower lobe. Chest X-ray shows a new right lower lobe infiltrate. Blood cultures are pending. Sputum Gram stain shows gram-negative rods. What is the most appropriate initial antibiotic regimen?