To tackle this problem, we first need to define the symbolic representation of the variables and the optimization problem itself. The variables are 'milligrams of vitamin E', 'milligrams of vitamin C', and 'milligrams of vitamin K'. Let's denote these as `x1`, `x2`, and `x3` respectively.

The objective function is to minimize `5.01*x1 + 5.67*x2 + 6.82*x3`.

Given constraints:
- The cognitive performance index for milligrams of vitamin E, C, and K are given but seem to be part of the resource/attributes description rather than direct constraints.
- Total combined cognitive performance index from `x1` (vitamin E) and `x2` (vitamin C) should be at least 7: `2*x1 + 2*x2 >= 7`.
- The total combined cognitive performance index from all three vitamins should be no less than 5: `2*x1 + 2*x2 + 5*x3 >= 5`.
- Another constraint repeats the condition that the total of all three should be at least 5, which seems redundant.
- `6*x1 - 6*x2 >= 0`.
- `-4*x2 + x3 >= 0`.
- The total cognitive performance index from `x1` and `x3` has to be at most 21: `2*x1 + 5*x3 <= 21`.
- The total cognitive performance index from `x2` and `x3` should not exceed 19: `2*x2 + 5*x3 <= 19`.

All variables can be non-integer.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin E'), ('x2', 'milligrams of vitamin C'), ('x3', 'milligrams of vitamin K')],
    'objective_function': 'minimize 5.01*x1 + 5.67*x2 + 6.82*x3',
    'constraints': [
        '2*x1 + 2*x2 >= 7',
        '2*x1 + 2*x2 + 5*x3 >= 5',
        '6*x1 - 6*x2 >= 0',
        '-4*x2 + x3 >= 0',
        '2*x1 + 5*x3 <= 21',
        '2*x2 + 5*x3 <= 19'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_E")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_C")
x3 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_K")

# Set the objective function
m.setObjective(5.01*x1 + 5.67*x2 + 6.82*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + 2*x2 >= 7, name="cognitive_performance_index_min")
m.addConstr(2*x1 + 2*x2 + 5*x3 >= 5, name="total_cognitive_performance_min")
m.addConstr(6*x1 - 6*x2 >= 0, name="vitamin_E_over_vitamin_C")
m.addConstr(-4*x2 + x3 >= 0, name="vitamin_C_and_vitamin_K_balance")
m.addConstr(2*x1 + 5*x3 <= 21, name="max_cognitive_performance_x1_x3")
m.addConstr(2*x2 + 5*x3 <= 19, name="max_cognitive_performance_x2_x3")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin E: {x1.x}")
    print(f"Milligrams of Vitamin C: {x2.x}")
    print(f"Milligrams of Vitamin K: {x3.x}")
else:
    print("No optimal solution found.")
```