## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'milligrams of vitamin B12'
- $x_1$ represents 'milligrams of vitamin B6'
- $x_2$ represents 'grams of carbohydrates'
- $x_3$ represents 'milligrams of zinc'

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $3x_0 + 7x_1 + 3x_2 + 3x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are as follows:
- $13x_0 \leq 172$
- $5x_0 \leq 115$
- $12x_0 \leq 105$
- $11x_1 \leq 172$
- $10x_1 \leq 115$
- $x_1 \leq 105$
- $11x_2 \leq 172$
- $8x_2 \leq 115$
- $4x_2 \leq 105$
- $11x_3 \leq 172$
- $8x_3 \leq 115$
- $5x_3 \leq 105$
- $13x_0 + 11x_3 \geq 38$
- $13x_0 + 11x_1 + 11x_3 \geq 37$
- $11x_1 + 11x_2 + 11x_3 \geq 37$
- $13x_0 + 11x_1 + 11x_3 \geq 24$
- $11x_1 + 11x_2 + 11x_3 \geq 24$
- $12x_0 + x_1 + 4x_2 \geq 24$
- $13x_0 + 11x_1 \leq 100$
- $11x_2 + 11x_3 \leq 87$
- $13x_0 + 11x_1 + 11x_2 + 11x_3 \leq 87$
- $10x_1 + 8x_3 \leq 85$
- $5x_0 + 8x_2 \leq 33$
- $10x_1 + 8x_2 \leq 86$
- $5x_0 + 8x_2 + 8x_3 \leq 51$
- $10x_1 + 8x_2 + 8x_3 \leq 87$
- $5x_0 + 10x_1 + 8x_3 \leq 97$
- $5x_0 + 10x_1 + 8x_2 + 8x_3 \leq 97$
- $4x_2 + 5x_3 \leq 85$
- $12x_0 + x_1 \leq 78$
- $x_1 + 5x_3 \leq 41$
- $12x_0 + x_1 + 5x_3 \leq 39$
- $12x_0 + 4x_2 + 5x_3 \leq 65$
- $12x_0 + x_1 + 4x_2 \leq 45$
- $12x_0 + x_1 + 4x_2 + 5x_3 \leq 45$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B12'),
        ('x1', 'milligrams of vitamin B6'),
        ('x2', 'grams of carbohydrates'),
        ('x3', 'milligrams of zinc')
    ],
    'objective_function': '3*x0 + 7*x1 + 3*x2 + 3*x3',
    'constraints': [
        '13*x0 <= 172',
        '5*x0 <= 115',
        '12*x0 <= 105',
        '11*x1 <= 172',
        '10*x1 <= 115',
        'x1 <= 105',
        '11*x2 <= 172',
        '8*x2 <= 115',
        '4*x2 <= 105',
        '11*x3 <= 172',
        '8*x3 <= 115',
        '5*x3 <= 105',
        '13*x0 + 11*x3 >= 38',
        '13*x0 + 11*x1 + 11*x3 >= 37',
        '11*x1 + 11*x2 + 11*x3 >= 37',
        '13*x0 + 11*x1 + 11*x3 >= 24',
        '11*x1 + 11*x2 + 11*x3 >= 24',
        '12*x0 + x1 + 4*x2 >= 24',
        '13*x0 + 11*x1 <= 100',
        '11*x2 + 11*x3 <= 87',
        '13*x0 + 11*x1 + 11*x2 + 11*x3 <= 87',
        '10*x1 + 8*x3 <= 85',
        '5*x0 + 8*x2 <= 33',
        '10*x1 + 8*x2 <= 86',
        '5*x0 + 8*x2 + 8*x3 <= 51',
        '10*x1 + 8*x2 + 8*x3 <= 87',
        '5*x0 + 10*x1 + 8*x3 <= 97',
        '5*x0 + 10*x1 + 8*x2 + 8*x3 <= 97',
        '4*x2 + 5*x3 <= 85',
        '12*x0 + x1 <= 78',
        'x1 + 5*x3 <= 41',
        '12*x0 + x1 + 5*x3 <= 39',
        '12*x0 + 4*x2 + 5*x3 <= 65',
        '12*x0 + x1 + 4*x2 <= 45',
        '12*x0 + x1 + 4*x2 + 5*x3 <= 45'
    ]
}
```

## 5: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # milligrams of vitamin B12
    x1 = model.addVar(name="x1", lb=0)  # milligrams of vitamin B6
    x2 = model.addVar(name="x2", lb=0)  # grams of carbohydrates
    x3 = model.addVar(name="x3", lb=0)  # milligrams of zinc

    # Objective function
    model.setObjective(3*x0 + 7*x1 + 3*x2 + 3*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(13*x0 <= 172)
    model.addConstr(5*x0 <= 115)
    model.addConstr(12*x0 <= 105)
    model.addConstr(11*x1 <= 172)
    model.addConstr(10*x1 <= 115)
    model.addConstr(x1 <= 105)
    model.addConstr(11*x2 <= 172)
    model.addConstr(8*x2 <= 115)
    model.addConstr(4*x2 <= 105)
    model.addConstr(11*x3 <= 172)
    model.addConstr(8*x3 <= 115)
    model.addConstr(5*x3 <= 105)
    model.addConstr(13*x0 + 11*x3 >= 38)
    model.addConstr(13*x0 + 11*x1 + 11*x3 >= 37)
    model.addConstr(11*x1 + 11*x2 + 11*x3 >= 37)
    model.addConstr(13*x0 + 11*x1 + 11*x3 >= 24)
    model.addConstr(11*x1 + 11*x2 + 11*x3 >= 24)
    model.addConstr(12*x0 + x1 + 4*x2 >= 24)
    model.addConstr(13*x0 + 11*x1 <= 100)
    model.addConstr(11*x2 + 11*x3 <= 87)
    model.addConstr(13*x0 + 11*x1 + 11*x2 + 11*x3 <= 87)
    model.addConstr(10*x1 + 8*x3 <= 85)
    model.addConstr(5*x0 + 8*x2 <= 33)
    model.addConstr(10*x1 + 8*x2 <= 86)
    model.addConstr(5*x0 + 8*x2 + 8*x3 <= 51)
    model.addConstr(10*x1 + 8*x2 + 8*x3 <= 87)
    model.addConstr(5*x0 + 10*x1 + 8*x3 <= 97)
    model.addConstr(5*x0 + 10*x1 + 8*x2 + 8*x3 <= 97)
    model.addConstr(4*x2 + 5*x3 <= 85)
    model.addConstr(12*x0 + x1 <= 78)
    model.addConstr(x1 + 5*x3 <= 41)
    model.addConstr(12*x0 + x1 + 5*x3 <= 39)
    model.addConstr(12*x0 + 4*x2 + 5*x3 <= 65)
    model.addConstr(12*x0 + x1 + 4*x2 <= 45)
    model.addConstr(12*x0 + x1 + 4*x2 + 5*x3 <= 45)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"milligrams of vitamin B12: {x0.varValue}")
        print(f"milligrams of vitamin B6: {x1.varValue}")
        print(f"grams of carbohydrates: {x2.varValue}")
        print(f"milligrams of zinc: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```