## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_1$ represents 'milligrams of vitamin C'
- $x_2$ represents 'grams of protein'
- $x_3$ represents 'milligrams of vitamin B7'
- $x_4$ represents 'milligrams of vitamin B1'

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is: 
$2.67x_1^2 + 7.7x_1x_2 + 5.67x_1x_4 + 3.59x_2^2 + 8.32x_2x_3 + 8.4x_2x_4 + 1.38x_3^2 + 6.33x_3x_4 + 1.3x_1 + 5.9x_2 + 6.26x_3 + 3.36x_4$

## 3: Define the constraints in symbolic notation
The constraints are:
- $10x_1 + 10x_2 + 6x_3 + 16x_4 \leq 246$ (energy stability index constraint)
- $10x_1 \leq 246$ 
- $10x_2 \leq 246$ 
- $6x_3 \leq 246$ 
- $16x_4 \leq 246$ 
- $10x_1^2 + 16x_4^2 \geq 22$
- $10x_1 + 6x_3 \geq 50$
- $10x_2 + 6x_3 \geq 44$
- $10x_1 + 10x_2 + 16x_4 \geq 42$
- $10x_1 + 6x_3 + 16x_4 \geq 42$
- $10x_2 + 6x_3 + 16x_4 \geq 42$
- $10x_1 + 10x_2 + 16x_4 \geq 30$
- $10x_1 + 6x_3 + 16x_4 \geq 30$
- $10x_2 + 6x_3 + 16x_4 \geq 30$
- $10x_1 + 10x_2 + 16x_4 \geq 38$
- $10x_1^2 + 6x_3^2 + 16x_4^2 \geq 38$
- $10x_2 + 6x_3 + 16x_4 \geq 38$
- $10x_1 + 10x_2 + 6x_3 + 16x_4 \geq 38$
- $-2x_3 + 3x_4 \geq 0$
- $10x_2 + 6x_3 \leq 104$
- $10x_1^2 + 10x_2^2 + 6x_3^2 \leq 118$

## 4: Create a JSON object representing the problem symbolically
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin C'), 
        ('x2', 'grams of protein'), 
        ('x3', 'milligrams of vitamin B7'), 
        ('x4', 'milligrams of vitamin B1')
    ], 
    'objective_function': '2.67*x1^2 + 7.7*x1*x2 + 5.67*x1*x4 + 3.59*x2^2 + 8.32*x2*x3 + 8.4*x2*x4 + 1.38*x3^2 + 6.33*x3*x4 + 1.3*x1 + 5.9*x2 + 6.26*x3 + 3.36*x4', 
    'constraints': [
        '10*x1 + 10*x2 + 6*x3 + 16*x4 <= 246',
        '10*x1^2 + 16*x4^2 >= 22',
        '10*x1 + 6*x3 >= 50',
        '10*x2 + 6*x3 >= 44',
        '10*x1 + 10*x2 + 16*x4 >= 42',
        '10*x1 + 6*x3 + 16*x4 >= 42',
        '10*x2 + 6*x3 + 16*x4 >= 42',
        '10*x1 + 10*x2 + 16*x4 >= 30',
        '10*x1 + 6*x3 + 16*x4 >= 30',
        '10*x2 + 6*x3 + 16*x4 >= 30',
        '10*x1 + 10*x2 + 16*x4 >= 38',
        '10*x1^2 + 6*x3^2 + 16*x4^2 >= 38',
        '10*x2 + 6*x3 + 16*x4 >= 38',
        '10*x1 + 10*x2 + 6*x3 + 16*x4 >= 38',
        '-2*x3 + 3*x4 >= 0',
        '10*x2 + 6*x3 <= 104',
        '10*x1^2 + 10*x2^2 + 6*x3^2 <= 118'
    ]
}
```

## 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='milligrams of vitamin C')
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='grams of protein')
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='milligrams of vitamin B7')
    x4 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='milligrams of vitamin B1')

    # Define the objective function
    model.setObjective(2.67*x1**2 + 7.7*x1*x2 + 5.67*x1*x4 + 3.59*x2**2 + 8.32*x2*x3 + 8.4*x2*x4 + 1.38*x3**2 + 6.33*x3*x4 + 1.3*x1 + 5.9*x2 + 6.26*x3 + 3.36*x4)

    # Add constraints
    model.addConstr(10*x1 + 10*x2 + 6*x3 + 16*x4 <= 246)
    model.addConstr(10*x1**2 + 16*x4**2 >= 22)
    model.addConstr(10*x1 + 6*x3 >= 50)
    model.addConstr(10*x2 + 6*x3 >= 44)
    model.addConstr(10*x1 + 10*x2 + 16*x4 >= 42)
    model.addConstr(10*x1 + 6*x3 + 16*x4 >= 42)
    model.addConstr(10*x2 + 6*x3 + 16*x4 >= 42)
    model.addConstr(10*x1 + 10*x2 + 16*x4 >= 30)
    model.addConstr(10*x1 + 6*x3 + 16*x4 >= 30)
    model.addConstr(10*x2 + 6*x3 + 16*x4 >= 30)
    model.addConstr(10*x1 + 10*x2 + 16*x4 >= 38)
    model.addConstr(10*x1**2 + 6*x3**2 + 16*x4**2 >= 38)
    model.addConstr(10*x2 + 6*x3 + 16*x4 >= 38)
    model.addConstr(10*x1 + 10*x2 + 6*x3 + 16*x4 >= 38)
    model.addConstr(-2*x3 + 3*x4 >= 0)
    model.addConstr(10*x2 + 6*x3 <= 104)
    model.addConstr(10*x1**2 + 10*x2**2 + 6*x3**2 <= 118)

    # Set the objective to minimize
    model.setAttr(gurobi.GRB.Attr.Sense, gurobi.GRB.MINIMIZE)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('x1: ', x1.varValue)
        print('x2: ', x2.varValue)
        print('x3: ', x3.varValue)
        print('x4: ', x4.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```