To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into a mathematical formulation. The goal is to maximize an objective function that combines milligrams of iron, vitamin C, and grams of fiber, subject to several constraints related to kidney support indices and cognitive performance indices.

### Mathematical Formulation

Let's denote:
- \(x_0\) as the amount of milligrams of iron,
- \(x_1\) as the amount of milligrams of vitamin C,
- \(x_2\) as the amount of grams of fiber.

The objective function to maximize is:
\[1.3x_0 + 6.78x_1 + 8.38x_2\]

Subject to the constraints:

1. Kidney support index for iron: \(33x_0\)
2. Cognitive performance index for iron: \(6x_0\)
3. Kidney support index for vitamin C: \(2x_1\)
4. Cognitive performance index for vitamin C: \(4x_1\)
5. Kidney support index for fiber: \(6x_2\)
6. Cognitive performance index for fiber: \(25x_2\)

And the following combined constraints:
- Total kidney support index from vitamin C and fiber: \(2x_1 + 6x_2 \geq 78\)
- Maximum total kidney support index from iron and fiber: \(33x_0 + 6x_2 \leq 331\)
- Maximum total kidney support index from vitamin C and fiber: \(2x_1 + 6x_2 \leq 166\)
- Maximum total kidney support index from all three: \(33x_0 + 2x_1 + 6x_2 \leq 166\)
- Maximum total cognitive performance index from vitamin C and fiber: \(4x_1 + 25x_2 \leq 87\)
- Maximum total cognitive performance index from iron and vitamin C: \(6x_0 + 4x_1 \leq 113\)
- Maximum total cognitive performance index from all three: \(6x_0 + 4x_1 + 25x_2 \leq 113\)

### Gurobi Code

```python
from gurobipy import *

# Create a new model
m = Model("Nutrient_Optimization")

# Define the variables
x0 = m.addVar(lb=0, name="milligrams_of_iron")
x1 = m.addVar(lb=0, name="milligrams_of_vitamin_C")
x2 = m.addVar(lb=0, name="grams_of_fiber")

# Objective function: Maximize
m.setObjective(1.3*x0 + 6.78*x1 + 8.38*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(2*x1 + 6*x2 >= 78, "kidney_support_vitamin_C_fiber_min")
m.addConstr(33*x0 + 6*x2 <= 331, "kidney_support_iron_fiber_max")
m.addConstr(2*x1 + 6*x2 <= 166, "kidney_support_vitamin_C_fiber_max")
m.addConstr(33*x0 + 2*x1 + 6*x2 <= 166, "total_kidney_support_max")
m.addConstr(4*x1 + 25*x2 <= 87, "cognitive_performance_vitamin_C_fiber_max")
m.addConstr(6*x0 + 4*x1 <= 113, "cognitive_performance_iron_vitamin_C_max")
m.addConstr(6*x0 + 4*x1 + 25*x2 <= 113, "total_cognitive_performance_max")

# Optimize the model
m.optimize()

# Print the results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
print(f"Objective: {m.objVal}")
```
```python 
```