## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of magnesium' and 'milligrams of vitamin B4', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $1.2x_1^2 + 6.74x_1x_2 + 5.86x_1 + 9.51x_2$.

## 3: Define the constraints in symbolic notation
The constraints given are:
- $6x_1 \leq 147$ (digestive support index of $x_1$)
- $15x_1 \leq 57$ (muscle growth index of $x_1$)
- $13x_2 \leq 147$ (digestive support index of $x_2$)
- $6x_2 \leq 57$ (muscle growth index of $x_2$)
- $6x_1^2 + 13x_2^2 \geq 48$ (total combined digestive support index from $x_1^2$ and $x_2^2$)
- $6x_1 + 13x_2 \geq 48$ (total combined digestive support index from $x_1$ and $x_2$)
- $15x_1^2 + 6x_2^2 \geq 24$ (total combined muscle growth index from $x_1^2$ and $x_2^2$)
- $15x_1 + 6x_2 \geq 24$ (total combined muscle growth index from $x_1$ and $x_2$)
- $-6x_1 + 8x_2 \geq 0$
- $6x_1 + 13x_2 \leq 96$ (total combined digestive support index from $x_1$ and $x_2$)
- $15x_1 + 6x_2 \leq 30$ (total combined muscle growth index from $x_1$ and $x_2$)

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'milligrams of magnesium'), ('x2', 'milligrams of vitamin B4')],
    'objective_function': '1.2*x1^2 + 6.74*x1*x2 + 5.86*x1 + 9.51*x2',
    'constraints': [
        '6*x1 <= 147',
        '15*x1 <= 57',
        '13*x2 <= 147',
        '6*x2 <= 57',
        '6*x1^2 + 13*x2^2 >= 48',
        '6*x1 + 13*x2 >= 48',
        '15*x1^2 + 6*x2^2 >= 24',
        '15*x1 + 6*x2 >= 24',
        '-6*x1 + 8*x2 >= 0',
        '6*x1 + 13*x2 <= 96',
        '15*x1 + 6*x2 <= 30'
    ]
}
```

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

def optimize_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="milligrams of magnesium", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="milligrams of vitamin B4", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

    # Objective function
    model.setObjective(1.2*x1**2 + 6.74*x1*x2 + 5.86*x1 + 9.51*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(6*x1 <= 147)
    model.addConstr(15*x1 <= 57)
    model.addConstr(13*x2 <= 147)
    model.addConstr(6*x2 <= 57)
    model.addConstr(6*x1**2 + 13*x2**2 >= 48)
    model.addConstr(6*x1 + 13*x2 >= 48)
    model.addConstr(15*x1**2 + 6*x2**2 >= 24)
    model.addConstr(15*x1 + 6*x2 >= 24)
    model.addConstr(-6*x1 + 8*x2 >= 0)
    model.addConstr(6*x1 + 13*x2 <= 96)
    model.addConstr(15*x1 + 6*x2 <= 30)

    # Optimize the model
    model.optimize()

    # Print the status of the optimization
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of magnesium: {x1.varValue}")
        print(f"Milligrams of vitamin B4: {x2.varValue}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("No feasible solution exists.")
    else:
        print("Optimization failed.")

optimize_problem()
```