A 7-year-old boy receiving chemotherapy for acute lymphoblastic leukaemia develops a temperature of 38.6°C at home. In hospital he is alert, has normal perfusion and no respiratory focus; his absolute neutrophil count is 0.2 × 10⁹/L (1.5–8.0), and he has a double-lumen central venous catheter. He has no history of resistant organisms or immediate antibiotic allergy. Which one of the following is the most appropriate initial antimicrobial treatment?