## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B3', 'grams of fiber', 'milligrams of vitamin K', 'grams of carbohydrates']. Let's denote them as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $4.8x_1^2 + 2.12x_1x_2 + 6.97x_1x_3 + 8.25x_2^2 + 7.81x_2x_3 + 3.96x_1 + 8.16x_2 + 7.57x_4$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $x_1 \geq 0$ (implicit, as there's no lower bound given)
2. $x_2 \geq 0$ (implicit, as there's no lower bound given)
3. $x_3 \geq 0$ (implicit, as there's no lower bound given)
4. $x_4 \geq 0$ (implicit, as there's no lower bound given)
5. $1x_1 + 5x_2 + 2x_3 + 2x_4 \leq 76$
6. $1x_1 \geq 1$ (cardiovascular support index for $x_1$)
7. $5x_2 \geq 5$ (cardiovascular support index for $x_2$)
8. $2x_3 \geq 2$ (cardiovascular support index for $x_3$)
9. $2x_4 \geq 2$ (cardiovascular support index for $x_4$)
10. $1x_1 + 2x_3 \geq 17$
11. $(2x_3)^2 + (2x_4)^2 \geq 17$
12. $1x_1 + 5x_2 \geq 12$
13. $1x_1 + 5x_2 + 2x_3 + 2x_4 \geq 12$
14. $-5x_1 + 3x_2 \geq 0$
15. $-x_1^2 + 2x_3^2 \geq 0$
16. $-2x_2 + 5x_3 + 2x_4 \geq 0$
17. $1x_1 + 2x_4 \leq 29$
18. $1x_1 + 5x_2 \leq 23$

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [
    ('x1', 'milligrams of vitamin B3'), 
    ('x2', 'grams of fiber'), 
    ('x3', 'milligrams of vitamin K'), 
    ('x4', 'grams of carbohydrates')
],
'objective_function': '4.8*x1^2 + 2.12*x1*x2 + 6.97*x1*x3 + 8.25*x2^2 + 7.81*x2*x3 + 3.96*x1 + 8.16*x2 + 7.57*x4',
'constraints': [
    'x1 >= 0', 'x2 >= 0', 'x3 >= 0', 'x4 >= 0',
    '1*x1 + 5*x2 + 2*x3 + 2*x4 <= 76',
    '1*x1 >= 1', '5*x2 >= 5', '2*x3 >= 2', '2*x4 >= 2',
    '1*x1 + 2*x3 >= 17',
    '(2*x3)^2 + (2*x4)^2 >= 17',
    '1*x1 + 5*x2 >= 12',
    '1*x1 + 5*x2 + 2*x3 + 2*x4 >= 12',
    '-5*x1 + 3*x2 >= 0',
    '-x1^2 + 2*x3^2 >= 0',
    '-2*x2 + 5*x3 + 2*x4 >= 0',
    '1*x1 + 2*x4 <= 29',
    '1*x1 + 5*x2 <= 23'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(lb=0, name="milligrams of vitamin B3")
    x2 = model.addVar(lb=0, name="grams of fiber")
    x3 = model.addVar(lb=0, name="milligrams of vitamin K")
    x4 = model.addVar(lb=0, name="grams of carbohydrates")

    # Objective function
    model.setObjective(4.8*x1**2 + 2.12*x1*x2 + 6.97*x1*x3 + 8.25*x2**2 + 7.81*x2*x3 + 3.96*x1 + 8.16*x2 + 7.57*x4)

    # Constraints
    model.addConstr(x1 + 5*x2 + 2*x3 + 2*x4 <= 76)
    model.addConstr(x1 >= 1)
    model.addConstr(5*x2 >= 5)
    model.addConstr(2*x3 >= 2)
    model.addConstr(2*x4 >= 2)
    model.addConstr(x1 + 2*x3 >= 17)
    model.addConstr((2*x3)**2 + (2*x4)**2 >= 17)
    model.addConstr(x1 + 5*x2 >= 12)
    model.addConstr(x1 + 5*x2 + 2*x3 + 2*x4 >= 12)
    model.addConstr(-5*x1 + 3*x2 >= 0)
    model.addConstr(-x1**2 + 2*x3**2 >= 0)
    model.addConstr(-2*x2 + 5*x3 + 2*x4 >= 0)
    model.addConstr(x1 + 2*x4 <= 29)
    model.addConstr(x1 + 5*x2 <= 23)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin B3: {x1.varValue}")
        print(f"Grams of fiber: {x2.varValue}")
        print(f"Milligrams of vitamin K: {x3.varValue}")
        print(f"Grams of carbohydrates: {x4.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```