Final answer:
Based on the symptoms of vomiting, visible peristaltic waves, and laboratory results, the infant is likely suffering from hypertrophic pyloric stenosis, a type of intestinal obstruction.
Step-by-step explanation:
The clinical presentation of a 4-week-old male infant with a history of vomiting after feedings and visible peristaltic waves suggests a diagnosis of hypertrophic pyloric stenosis (HPS), which is a form of intestinal obstruction. The laboratory results show hypokalemia (low potassium) and hyponatremia (low sodium), which are consistent with the vomiting and potential dehydration seen in HPS. The history of projectile vomiting, palpable 'olive' in the epigastrium during physical examination, and the laboratory findings support this diagnosis over gastroenteritis, gastroesophageal reflux disease (GERD), or appendicitis, which do not typically present with this characteristic clinical picture in an infant this young.