Step 1: BPD is graded in infants born at less than 32 weeks gestation by what respiratory support they need at 36 weeks corrected gestational age (or at discharge, whichever is first). The grade reflects the support requirement assessed at that single time point, not the support needed earlier in life.
Step 2: Work out the timeline. The baby was born at 27 weeks. Mechanical ventilation continued for 4 weeks, taking him to 31 weeks corrected age. Oxygen was then given for 1 more week (up to 32 weeks corrected age). After that he was on room air.
Step 3: Therefore by 36 weeks corrected gestational age, the assessment time point, the baby is breathing room air. Needing oxygen or positive pressure earlier does not raise the grade because grading depends on the 36-week status.
Step 4: Room air at 36 weeks in a baby who needed supplemental oxygen for at least 28 days defines mild BPD. Moderate BPD would need <30% oxygen at 36 weeks, and severe BPD would need >=30% oxygen or positive pressure at 36 weeks, neither of which applies. So the answer is mild BPD.