Final answer:
The physician should see the patient with chest pain and shortness of breath first, as this may indicate a life-threatening condition requiring immediate attention.
Step-by-step explanation:
The physician should prioritize patients based on the severity and potential life-threatening nature of their conditions, which is a principle of triage. In this scenario, the physician should see the patient with chest pain and shortness of breath first. This patient may be experiencing a medical emergency such as a heart attack or pulmonary embolism, which requires immediate attention. The symptoms indicate a potentially serious condition that could be life-threatening, whereas the other patients with minor cut, headache, or sprained ankle likely do not face immediate danger.