To solve this optimization problem, we first need to define the variables, objective function, and constraints using Gurobi's Python interface.

### Problem Definition

The problem is to minimize the objective function:

\[ 8.11x_0 + 2.51x_1 + 1.72x_2 + 8.54x_3 + 2.94x_4 + 9.14x_5 \]

subject to numerous constraints.

### Gurobi Code

```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(lb=0, name="milligrams of vitamin B9")  # milligrams of vitamin B9
x1 = model.addVar(lb=0, name="milligrams of vitamin B6")  # milligrams of vitamin B6
x2 = model.addVar(lb=0, name="milligrams of vitamin K")   # milligrams of vitamin K
x3 = model.addVar(lb=0, name="milligrams of iron")        # milligrams of iron
x4 = model.addVar(lb=0, name="milligrams of vitamin B4")  # milligrams of vitamin B4
x5 = model.addVar(lb=0, name="grams of fiber")            # grams of fiber

# Objective function
model.setObjective(8.11*x0 + 2.51*x1 + 1.72*x2 + 8.54*x3 + 2.94*x4 + 9.14*x5, gurobi.GRB.MINIMIZE)

# Constraints
# Cardiovascular support index constraints
model.addConstr(6.31*x0 <= 511, name="cardiovascular support index of vitamin B9")
model.addConstr(11.01*x0 <= 699, name="digestive support index of vitamin B9")
model.addConstr(5.04*x1 <= 511, name="cardiovascular support index of vitamin B6")
model.addConstr(4.26*x1 <= 699, name="digestive support index of vitamin B6")
model.addConstr(5.01*x2 <= 511, name="cardiovascular support index of vitamin K")
model.addConstr(10.34*x2 <= 699, name="digestive support index of vitamin K")
model.addConstr(8.37*x3 <= 511, name="cardiovascular support index of iron")
model.addConstr(6.88*x3 <= 699, name="digestive support index of iron")
model.addConstr(6.46*x4 <= 511, name="cardiovascular support index of vitamin B4")
model.addConstr(10.93*x4 <= 699, name="digestive support index of vitamin B4")
model.addConstr(7.59*x5 <= 511, name="cardiovascular support index of fiber")
model.addConstr(9.82*x5 <= 699, name="digestive support index of fiber")

# Additional cardiovascular support index constraints
model.addConstr(5.04*x1 + 8.37*x3 >= 30)
model.addConstr(5.01*x2 + 8.37*x3 >= 68)
model.addConstr(6.31*x0 + 7.59*x5 >= 54)
model.addConstr(5.04*x1 + 6.46*x4 >= 30)
model.addConstr(6.31*x0 + 5.01*x2 + 6.46*x4 >= 75)
model.addConstr(6.31*x0 + 8.37*x3 + 7.59*x5 >= 75)
model.addConstr(6.31*x0 + 5.04*x1 + 8.37*x3 >= 75)
model.addConstr(6.31*x0 + 8.37*x3 + 6.46*x4 >= 75)
model.addConstr(8.37*x3 + 6.46*x4 + 7.59*x5 >= 75)
model.addConstr(5.04*x1 + 5.01*x2 + 6.46*x4 >= 75)
model.addConstr(5.01*x2 + 8.37*x3 + 6.46*x4 >= 75)
model.addConstr(5.04*x1 + 5.01*x2 + 7.59*x5 >= 75)
model.addConstr(6.31*x0 + 5.04*x1 + 7.59*x5 >= 75)

# Digestive support index constraints
model.addConstr(11.01*x0 + 4.26*x1 >= 63)
model.addConstr(10.93*x4 + 9.82*x5 >= 93)
model.addConstr(10.34*x2 + 9.82*x5 >= 63)
model.addConstr(11.01*x0 + 9.82*x5 >= 77)
model.addConstr(11.01*x0 + 4.26*x1 + 10.34*x2 + 6.88*x3 + 10.93*x4 + 9.82*x5 >= 77)

# Linear constraints
model.addConstr(5*x1 - 8*x3 >= 0)

# Upper bound constraints
model.addConstr(6.31*x0 + 7.59*x5 <= 267)
model.addConstr(6.31*x0 + 8.37*x3 + 6.46*x4 <= 468)
model.addConstr(6.31*x0 + 5.04*x1 + 5.01*x2 <= 486)
model.addConstr(5.04*x1 + 5.01*x2 + 6.46*x4 <= 364)
model.addConstr(5.01*x2 + 10.93*x4 + 9.82*x5 <= 375)
model.addConstr(6.31*x0 + 5.04*x1 + 7.59*x5 <= 476)

model.addConstr(11.01*x0 + 4.26*x1 <= 206)
model.addConstr(11.01*x0 + 10.34*x2 <= 675)
model.addConstr(10.34*x2 + 9.82*x5 <= 670)
model.addConstr(10.93*x4 + 9.82*x5 <= 385)
model.addConstr(4.26*x1 + 10.34*x2 <= 613)
model.addConstr(10.34*x2 + 10.93*x4 <= 538)
model.addConstr(4.26*x1 + 10.93*x4 <= 270)
model.addConstr(4.26*x1 + 6.88*x3 <= 377)
model.addConstr(4.26*x1 + 9.82*x5 <= 286)

# Optimize the model
model.optimize()

# Print the results
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Milligrams of vitamin B9: ", x0.x)
    print("Milligrams of vitamin B6: ", x1.x)
    print("Milligrams of vitamin K: ", x2.x)
    print("Milligrams of iron: ", x3.x)
    print("Milligrams of vitamin B4: ", x4.x)
    print("Grams of fiber: ", x5.x)
else:
    print("The model is infeasible")
```