To solve the given optimization problem, we need to define the variables, objective function, and constraints according to the provided description. The problem involves minimizing an objective function subject to various linear constraints.

Let's denote:
- $x_0$ as the milligrams of vitamin B3,
- $x_1$ as the milligrams of vitamin B9,
- $x_2$ as the milligrams of vitamin B5, and
- $x_3$ as the milligrams of vitamin B7.

The objective function to be minimized is:
\[ 7x_0 + 6x_1 + 9x_2 + 8x_3 \]

Given constraints are based on cognitive performance indices and digestive support indices. However, for simplicity and adherence to the problem statement, we'll directly translate the given conditions into Gurobi code without explicitly listing all constraints here due to their extensive nature.

Here's how you can represent this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables (all are continuous)
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='milligrams_of_vitamin_B3')
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='milligrams_of_vitamin_B9')
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='milligrams_of_vitamin_B5')
x3 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='milligrams_of_vitamin_B7')

# Objective function
m.setObjective(7*x0 + 6*x1 + 9*x2 + 8*x3, GRB.MINIMIZE)

# Constraints based on the description (example constraints)
# Cognitive performance index constraints
m.addConstr(x0 + x3 >= 32, name='cognitive_performance_B3_B7')
m.addConstr(x1 + x3 >= 17, name='cognitive_performance_B9_B7')
m.addConstr(x2 + x3 >= 40, name='cognitive_performance_B5_B7')
m.addConstr(x0 + x1 >= 44, name='cognitive_performance_B3_B9')
m.addConstr(x1 + x2 >= 19, name='cognitive_performance_B9_B5')
m.addConstr(x0 + x1 + x2 + x3 >= 19, name='total_cognitive_performance')

# Digestive support index constraints
m.addConstr(11*x0 + 12*x2 >= 43, name='digestive_support_B3_B5')
m.addConstr(16*x1 + 12*x2 >= 51, name='digestive_support_B9_B5')
m.addConstr(11*x0 + 14*x3 >= 52, name='digestive_support_B3_B7')
m.addConstr(11*x0 + 16*x1 + 12*x2 >= 35, name='total_digestive_support_B3_B9_B5')
m.addConstr(11*x0 + 16*x1 + 12*x2 + 12*x3 >= 35, name='total_digestive_support')

# Additional constraints
m.addConstr(-x0 + 8*x1 >= 0, name='additional_constraint_1')
m.addConstr(-5*x2 + x3 >= 0, name='additional_constraint_2')
m.addConstr(-8*x1 + 6*x3 >= 0, name='additional_constraint_3')

# Upper bounds for cognitive performance indices
m.addConstr(x1 + x3 <= 147, name='upper_bound_cognitive_B9_B7')
m.addConstr(x0 + x1 <= 191, name='upper_bound_cognitive_B3_B9')
m.addConstr(x0 + x3 <= 102, name='upper_bound_cognitive_B3_B7')
m.addConstr(x2 + x3 <= 160, name='upper_bound_cognitive_B5_B7')
m.addConstr(x0 + x2 <= 92, name='upper_bound_cognitive_B3_B5')
m.addConstr(x0 + x2 + x3 <= 185, name='upper_bound_total_cognitive_B3_B5_B7')

# Upper bounds for digestive support indices
m.addConstr(11*x0 + 16*x1 <= 230, name='upper_bound_digestive_B3_B9')
m.addConstr(16*x1 + 12*x2 <= 144, name='upper_bound_digestive_B9_B5')
m.addConstr(16*x1 + 12*x3 <= 227, name='upper_bound_digestive_B9_B7')
m.addConstr(11*x0 + 14*x3 <= 151, name='upper_bound_digestive_B3_B7')

# Optimize the model
m.optimize()

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

print(f"Objective: {m.objVal}")
```