**Core Concept**
In this question, we are looking for a muscle relaxant that can be safely used in a patient with liver dysfunction (indicated by high serum bilirubin) and renal impairment (indicated by high serum creatinine). This requires an understanding of the pharmacokinetics and metabolism of various muscle relaxants.

**Why the Correct Answer is Right**
The correct answer is Rocuronium, as it is primarily metabolized by the liver but its active metabolite is not significantly affected by liver dysfunction. Additionally, Rocuronium is not significantly excreted by the kidneys, making it a suitable choice for patients with renal impairment.

**Why Each Wrong Option is Incorrect**
**Option A:** Vecuronium - Vecuronium is metabolized by the liver, but its active metabolite is also significantly affected by liver dysfunction, making it less suitable for this patient.

**Option B:** Pancuronium - Pancuronium is primarily excreted by the kidneys, which could lead to accumulation and prolonged paralysis in a patient with renal impairment.

**Option C:** Atracurium - Atracurium is metabolized by ester hydrolysis and Hofmann elimination, but it can accumulate in patients with liver dysfunction and renal impairment, leading to prolonged paralysis.

**Clinical Pearl / High-Yield Fact**
Remember that Rocuronium is a good choice for patients with liver dysfunction and renal impairment, but it can cause histamine release and hypotension, especially in patients with liver disease.

**Correct Answer:** C. Rocuronium