## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_0$ represents milligrams of vitamin C
- $x_1$ represents milligrams of calcium
- $x_2$ represents milligrams of vitamin B5
- $x_3$ represents milligrams of vitamin A

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $3x_0 + 7x_1 + 9x_2 + 3x_3$.

## 3: List the constraints in symbolic notation
Constraints:
1. $0.35x_0 + 0.01x_2 + 0.43x_3 \geq 11$
2. $0.94x_1 + 0.01x_2 \geq 13$
3. $0.35x_0 + 0.94x_1 \geq 24$
4. $0.35x_0 + 0.94x_1 + 0.43x_3 \geq 16$
5. $0.35x_0 + 0.94x_1 + 0.01x_2 + 0.43x_3 \geq 16$
6. $0.65x_1 + 0.81x_3 \geq 27$
7. $0.46x_0 + 0.34x_2 \geq 20$
8. $0.46x_0 + 0.81x_3 \geq 14$
9. $0.46x_0 + 0.65x_1 \geq 12$
10. $0.46x_0 + 0.65x_1 + 0.34x_2 + 0.81x_3 \geq 12$
11. $-x_0 + 2x_1 \geq 0$
12. $0.35x_0 + 0.43x_3 \leq 55$
13. $0.35x_0 + 0.01x_2 \leq 87$
14. $0.35x_0 + 0.94x_1 \leq 86$
15. $0.35x_0 + 0.01x_2 + 0.43x_3 \leq 87$
16. $0.35x_0 + 0.94x_1 + 0.01x_2 \leq 34$
17. $0.35x_0 + 0.94x_1 + 0.43x_3 \leq 78$
18. $0.46x_0 + 0.34x_2 + 0.81x_3 \leq 39$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin C'), 
        ('x1', 'milligrams of calcium'), 
        ('x2', 'milligrams of vitamin B5'), 
        ('x3', 'milligrams of vitamin A')
    ], 
    'objective_function': '3*x0 + 7*x1 + 9*x2 + 3*x3', 
    'constraints': [
        '0.35*x0 + 0.01*x2 + 0.43*x3 >= 11',
        '0.94*x1 + 0.01*x2 >= 13',
        '0.35*x0 + 0.94*x1 >= 24',
        '0.35*x0 + 0.94*x1 + 0.43*x3 >= 16',
        '0.35*x0 + 0.94*x1 + 0.01*x2 + 0.43*x3 >= 16',
        '0.65*x1 + 0.81*x3 >= 27',
        '0.46*x0 + 0.34*x2 >= 20',
        '0.46*x0 + 0.81*x3 >= 14',
        '0.46*x0 + 0.65*x1 >= 12',
        '0.46*x0 + 0.65*x1 + 0.34*x2 + 0.81*x3 >= 12',
        '-x0 + 2*x1 >= 0',
        '0.35*x0 + 0.43*x3 <= 55',
        '0.35*x0 + 0.01*x2 <= 87',
        '0.35*x0 + 0.94*x1 <= 86',
        '0.35*x0 + 0.01*x2 + 0.43*x3 <= 87',
        '0.35*x0 + 0.94*x1 + 0.01*x2 <= 34',
        '0.35*x0 + 0.94*x1 + 0.43*x3 <= 78',
        '0.46*x0 + 0.34*x2 + 0.81*x3 <= 39'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x0")  # milligrams of vitamin C
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x1")  # milligrams of calcium
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x2")  # milligrams of vitamin B5
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x3")  # milligrams of vitamin A

    # Objective function
    model.setObjective(3*x0 + 7*x1 + 9*x2 + 3*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(0.35*x0 + 0.01*x2 + 0.43*x3 >= 11)
    model.addConstr(0.94*x1 + 0.01*x2 >= 13)
    model.addConstr(0.35*x0 + 0.94*x1 >= 24)
    model.addConstr(0.35*x0 + 0.94*x1 + 0.43*x3 >= 16)
    model.addConstr(0.35*x0 + 0.94*x1 + 0.01*x2 + 0.43*x3 >= 16)
    model.addConstr(0.65*x1 + 0.81*x3 >= 27)
    model.addConstr(0.46*x0 + 0.34*x2 >= 20)
    model.addConstr(0.46*x0 + 0.81*x3 >= 14)
    model.addConstr(0.46*x0 + 0.65*x1 >= 12)
    model.addConstr(0.46*x0 + 0.65*x1 + 0.34*x2 + 0.81*x3 >= 12)
    model.addConstr(-x0 + 2*x1 >= 0)
    model.addConstr(0.35*x0 + 0.43*x3 <= 55)
    model.addConstr(0.35*x0 + 0.01*x2 <= 87)
    model.addConstr(0.35*x0 + 0.94*x1 <= 86)
    model.addConstr(0.35*x0 + 0.01*x2 + 0.43*x3 <= 87)
    model.addConstr(0.35*x0 + 0.94*x1 + 0.01*x2 <= 34)
    model.addConstr(0.35*x0 + 0.94*x1 + 0.43*x3 <= 78)
    model.addConstr(0.46*x0 + 0.34*x2 + 0.81*x3 <= 39)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"x0 (milligrams of vitamin C): {x0.varValue}")
        print(f"x1 (milligrams of calcium): {x1.varValue}")
        print(f"x2 (milligrams of vitamin B5): {x2.varValue}")
        print(f"x3 (milligrams of vitamin A): {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```