**Core Concept**
The patient's condition is characterized by sepsis-induced vasodilation, leading to a decrease in systemic vascular resistance (SVR) and a compensatory increase in cardiac output. This results in a hyperdynamic state, often referred to as warm septic shock. The patient's acute renal failure and oliguria are likely due to prerenal causes, such as hypovolemia and decreased renal perfusion.

**Why the Correct Answer is Right**
Dopamine is a catecholamine with dose-dependent effects on the cardiovascular system. At low doses (1-2 μg/kg/min), dopamine increases renal blood flow and glomerular filtration rate (GFR) by dilating renal afferent arterioles and increasing cardiac output. This is particularly beneficial in patients with sepsis-induced vasodilation and prerenal acute kidney injury. At higher doses (5-10 μg/kg/min), dopamine increases SVR and cardiac contractility, which can be useful in treating hypotension. However, in this scenario, the patient's increased cardiac output and decreased SVR indicate that the primary goal is to support renal perfusion, making low-dose dopamine an appropriate choice.

**Why Each Wrong Option is Incorrect**

**Option A:** Norepinephrine is a potent vasoconstrictor that increases SVR and cardiac contractility, making it more suitable for treating hypotension in septic shock. However, it may worsen renal perfusion and is not indicated for acute renal failure.

**Option B:** Vasopressin is a vasoconstrictor that increases SVR and is often used in combination with norepinephrine to treat refractory septic shock. However, its effects on renal perfusion are unpredictable, and it is not the first-line choice for treating acute renal failure.

**Option C:** Furosemide is a loop diuretic that increases urine output but does not address the underlying cause of acute renal failure in this scenario. In fact, furosemide can worsen hypovolemia and decrease renal perfusion.

**Clinical Pearl / High-Yield Fact**
In sepsis-induced vasodilation, the primary goal is to support renal perfusion and increase GFR. Dopamine's dose-dependent effects make it an attractive choice for this scenario, but it's essential to carefully titrate the dose to avoid excessive vasoconstriction.

**Correct Answer:** C. Low-dose dopamine.