To capture the described optimization problem in Gurobi code, we first need to understand and translate the given objective function and constraints into a mathematical model that can be represented using linear programming (LP) or mixed-integer linear programming (MILP), depending on the nature of the variables. Given the problem statement, all variables are continuous, allowing us to use LP.

The objective function aims to maximize:
\[ 9.26 \times \text{milligrams of vitamin B12} + 9.94 \times \text{milligrams of vitamin D} + 6.7 \times \text{milligrams of vitamin C} \]

Subject to the constraints:

1. \( \text{milligrams of vitamin B12} \times 1 + \text{milligrams of vitamin D} \times 1 + \text{milligrams of vitamin C} \times 7 \geq 31 \)
2. \( -5 \times \text{milligrams of vitamin D} + 6 \times \text{milligrams of vitamin C} \geq 0 \)
3. \( \text{milligrams of vitamin B12} \times 1 + \text{milligrams of vitamin C} \times 7 \leq 130 \)
4. \( \text{milligrams of vitamin B12} \times 1 + \text{milligrams of vitamin D} \times 1 \leq 71 \)
5. \( \text{milligrams of vitamin B12} \times 1 + \text{milligrams of vitamin D} \times 1 + \text{milligrams of vitamin C} \times 7 \leq 71 \)

Let's denote:
- \( x_0 = \text{milligrams of vitamin B12} \)
- \( x_1 = \text{milligrams of vitamin D} \)
- \( x_2 = \text{milligrams of vitamin C} \)

Given this notation, the model can be directly translated into Gurobi code. Note that all variables are continuous, so we don't need to specify them as integers.

```python
from gurobipy import *

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

# Create variables
x0 = m.addVar(lb=0, name="milligrams_of_vitamin_B12", vtype=GRB.CONTINUOUS)
x1 = m.addVar(lb=0, name="milligrams_of_vitamin_D", vtype=GRB.CONTINUOUS)
x2 = m.addVar(lb=0, name="milligrams_of_vitamin_C", vtype=GRB.CONTINUOUS)

# Set the objective function
m.setObjective(9.26*x0 + 9.94*x1 + 6.7*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x0 + x1 + 7*x2 >= 31, name="cognitive_performance_index_min")
m.addConstr(-5*x1 + 6*x2 >= 0, name="vitamin_D_and_C_constraint")
m.addConstr(x0 + 7*x2 <= 130, name="vitamin_B12_and_C_max")
m.addConstr(x0 + x1 <= 71, name="vitamin_B12_and_D_max")
m.addConstr(x0 + x1 + 7*x2 <= 71, name="total_cognitive_performance_index_max")

# Optimize the model
m.optimize()

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