To convert the natural language description of the optimization problem into functional Gurobi code, we need to follow these steps:

1. Define the variables: We have two variables - `grams_of_fat` and `milligrams_of_vitamin_C`.
2. Define the objective function: The objective is to minimize `8 * grams_of_fat + 4 * milligrams_of_vitamin_C`.
3. Define the constraints:
   - The digestive support index for `grams_of_fat` is 14, and for `milligrams_of_vitamin_C` is 12.
   - The cognitive performance index of `grams_of_fat` is 7, and for `milligrams_of_vitamin_C` is 15.
   - The total combined digestive support index should be greater than or equal to 21.
   - The total combined cognitive performance index should be at least 38.
   - `-1 * grams_of_fat + 6 * milligrams_of_vitamin_C >= 0`.
   - The maximum total combined digestive support index is 71.
   - The maximum total combined cognitive performance index is 88.

Given the problem description, we can directly translate these requirements into Gurobi code. Note that the constraints related to the indices are already accounted for in the bounds and coefficients of other constraints, so they don't need separate constraint definitions.

```python
from gurobipy import *

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

# Define variables
grams_of_fat = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="grams_of_fat")
milligrams_of_vitamin_C = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_C")

# Define objective function
m.setObjective(8 * grams_of_fat + 4 * milligrams_of_vitamin_C, GRB.MINIMIZE)

# Define constraints
m.addConstr(14 * grams_of_fat + 12 * milligrams_of_vitamin_C >= 21, name="digestive_support_index_min")
m.addConstr(14 * grams_of_fat + 12 * milligrams_of_vitamin_C <= 71, name="digestive_support_index_max")
m.addConstr(7 * grams_of_fat + 15 * milligrams_of_vitamin_C >= 38, name="cognitive_performance_index_min")
m.addConstr(7 * grams_of_fat + 15 * milligrams_of_vitamin_C <= 88, name="cognitive_performance_index_max")
m.addConstr(-1 * grams_of_fat + 6 * milligrams_of_vitamin_C >= 0, name="additional_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of fat: {grams_of_fat.x}")
    print(f"Milligrams of vitamin C: {milligrams_of_vitamin_C.x}")
else:
    print("No optimal solution found")
```