## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'milligrams of calcium', 'grams of carbohydrates', and 'milligrams of vitamin B4', which we can denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $3.0x_1^2 + 9.58x_1x_2 + 7.74x_1x_3 + 1.46x_2x_3 + 8.91x_3^2$.

## 3: List the constraints in symbolic notation
The constraints are:
- $3x_1 \leq 334$
- $24x_1 \leq 327$
- $17x_1 \leq 156$
- $14x_1 \leq 213$
- $23x_1 \leq 316$
- $21x_2 \leq 334$
- $6x_2 \leq 327$
- $20x_2 \leq 156$
- $25x_2 \leq 213$
- $4x_2 \leq 316$
- $21x_3 \leq 334$
- $29x_3 \leq 327$
- $23x_3 \leq 156$
- $25x_3 \leq 213$
- $15x_3 \leq 316$
- $3x_1 + 21x_3 \geq 91$
- $3x_1 + 21x_2 \geq 86$
- $17x_1 + 20x_2 + 23x_3 \geq 41$
- $14x_1^2 + 25x_2^2 \geq 62$
- $25x_2 + 25x_3 \geq 52$
- $4x_2^2 + 15x_3^2 \geq 88$
- $23x_1 + 4x_2 + 15x_3 \geq 55$
- $3x_1 + 21x_2 \leq 257$
- $3x_1 + 21x_3 \leq 257$
- $3x_1 + 21x_2 + 21x_3 \leq 257$
- $6x_2^2 + 29x_3^2 \leq 214$
- $24x_1^2 + 6x_2^2 \leq 230$
- $24x_1 + 6x_2 + 29x_3 \leq 230$
- $17x_1 + 23x_3 \leq 83$
- $17x_1 + 20x_2 + 23x_3 \leq 83$
- $14x_1 + 25x_2 \leq 76$
- $25x_2 + 25x_3 \leq 158$
- $14x_1^2 + 25x_3^2 \leq 181$
- $14x_1 + 25x_2 + 25x_3 \leq 181$
- $23x_1^2 + 15x_3^2 \leq 163$
- $23x_1 + 4x_2 \leq 220$
- $4x_2 + 15x_3 \leq 309$
- $23x_1 + 4x_2 + 15x_3 \leq 309$

## 4: Define the symbolic variables and constraints for the JSON output
```json
{
    'sym_variables': [
        ('x1', 'milligrams of calcium'), 
        ('x2', 'grams of carbohydrates'), 
        ('x3', 'milligrams of vitamin B4')
    ], 
    'objective_function': '3.0*x1^2 + 9.58*x1*x2 + 7.74*x1*x3 + 1.46*x2*x3 + 8.91*x3^2', 
    'constraints': [
        '3*x1 <= 334',
        '24*x1 <= 327',
        '17*x1 <= 156',
        '14*x1 <= 213',
        '23*x1 <= 316',
        '21*x2 <= 334',
        '6*x2 <= 327',
        '20*x2 <= 156',
        '25*x2 <= 213',
        '4*x2 <= 316',
        '21*x3 <= 334',
        '29*x3 <= 327',
        '23*x3 <= 156',
        '25*x3 <= 213',
        '15*x3 <= 316',
        '3*x1 + 21*x3 >= 91',
        '3*x1 + 21*x2 >= 86',
        '17*x1 + 20*x2 + 23*x3 >= 41',
        '14*x1^2 + 25*x2^2 >= 62',
        '25*x2 + 25*x3 >= 52',
        '4*x2^2 + 15*x3^2 >= 88',
        '23*x1 + 4*x2 + 15*x3 >= 55',
        '3*x1 + 21*x2 <= 257',
        '3*x1 + 21*x3 <= 257',
        '3*x1 + 21*x2 + 21*x3 <= 257',
        '6*x2^2 + 29*x3^2 <= 214',
        '24*x1^2 + 6*x2^2 <= 230',
        '24*x1 + 6*x2 + 29*x3 <= 230',
        '17*x1 + 23*x3 <= 83',
        '17*x1 + 20*x2 + 23*x3 <= 83',
        '14*x1 + 25*x2 <= 76',
        '25*x2 + 25*x3 <= 158',
        '14*x1^2 + 25*x3^2 <= 181',
        '14*x1 + 25*x2 + 25*x3 <= 181',
        '23*x1^2 + 15*x3^2 <= 163',
        '23*x1 + 4*x2 <= 220',
        '4*x2 + 15*x3 <= 309',
        '23*x1 + 4*x2 + 15*x3 <= 309'
    ]
}
```

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

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

    # Define variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams of calcium")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="grams of carbohydrates")
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams of vitamin B4")

    # Objective function
    model.setObjective(3.0*x1**2 + 9.58*x1*x2 + 7.74*x1*x3 + 1.46*x2*x3 + 8.91*x3**2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3*x1 <= 334)
    model.addConstr(24*x1 <= 327)
    model.addConstr(17*x1 <= 156)
    model.addConstr(14*x1 <= 213)
    model.addConstr(23*x1 <= 316)
    model.addConstr(21*x2 <= 334)
    model.addConstr(6*x2 <= 327)
    model.addConstr(20*x2 <= 156)
    model.addConstr(25*x2 <= 213)
    model.addConstr(4*x2 <= 316)
    model.addConstr(21*x3 <= 334)
    model.addConstr(29*x3 <= 327)
    model.addConstr(23*x3 <= 156)
    model.addConstr(25*x3 <= 213)
    model.addConstr(15*x3 <= 316)
    model.addConstr(3*x1 + 21*x3 >= 91)
    model.addConstr(3*x1 + 21*x2 >= 86)
    model.addConstr(17*x1 + 20*x2 + 23*x3 >= 41)
    model.addConstr(14*x1**2 + 25*x2**2 >= 62)
    model.addConstr(25*x2 + 25*x3 >= 52)
    model.addConstr(4*x2**2 + 15*x3**2 >= 88)
    model.addConstr(23*x1 + 4*x2 + 15*x3 >= 55)
    model.addConstr(3*x1 + 21*x2 <= 257)
    model.addConstr(3*x1 + 21*x3 <= 257)
    model.addConstr(3*x1 + 21*x2 + 21*x3 <= 257)
    model.addConstr(6*x2**2 + 29*x3**2 <= 214)
    model.addConstr(24*x1**2 + 6*x2**2 <= 230)
    model.addConstr(24*x1 + 6*x2 + 29*x3 <= 230)
    model.addConstr(17*x1 + 23*x3 <= 83)
    model.addConstr(17*x1 + 20*x2 + 23*x3 <= 83)
    model.addConstr(14*x1 + 25*x2 <= 76)
    model.addConstr(25*x2 + 25*x3 <= 158)
    model.addConstr(14*x1**2 + 25*x3**2 <= 181)
    model.addConstr(14*x1 + 25*x2 + 25*x3 <= 181)
    model.addConstr(23*x1**2 + 15*x3**2 <= 163)
    model.addConstr(23*x1 + 4*x2 <= 220)
    model.addConstr(4*x2 + 15*x3 <= 309)
    model.addConstr(23*x1 + 4*x2 + 15*x3 <= 309)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Milligrams of calcium: ", x1.varValue)
        print("Grams of carbohydrates: ", x2.varValue)
        print("Milligrams of vitamin B4: ", x3.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```