## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ represents 'milligrams of vitamin B4'
- $x_2$ represents 'milligrams of iron'
- $x_3$ represents 'milligrams of vitamin B3'
- $x_4$ represents 'milligrams of calcium'

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $8x_1 + 5x_2 + 3x_3 + 6x_4$.

## Step 3: List all the constraints in symbolic notation
The constraints are:
1. $10x_1 \geq 0$ (Implicit, as $x_1$ is non-negative)
2. $6x_2 \geq 0$ (Implicit, as $x_2$ is non-negative)
3. $x_3 \geq 0$ (Implicit, as $x_3$ is non-negative)
4. $9x_4 \geq 0$ (Implicit, as $x_4$ is non-negative)
5. $10x_1 + x_3 \geq 88$
6. $6x_2 + x_3 \geq 45$
7. $10x_1 + 6x_2 \geq 104$
8. $6x_2 + 9x_4 \geq 124$
9. $10x_1 + 6x_2 + 9x_4 \geq 88$
10. $10x_1 + 6x_2 + x_3 \geq 88$
11. $10x_1 + x_3 + 9x_4 \geq 88$
12. $10x_1 + 6x_2 + 9x_4 \geq 106$
13. $10x_1 + 6x_2 + x_3 \geq 106$
14. $10x_1 + x_3 + 9x_4 \geq 106$
15. $10x_1 + 6x_2 + 9x_4 \geq 81$
16. $10x_1 + 6x_2 + x_3 \geq 81$
17. $10x_1 + x_3 + 9x_4 \geq 81$
18. $10x_1 + 6x_2 + x_3 + 9x_4 \geq 81$
19. $-2x_2 + 2x_3 \geq 0$
20. $10x_1 + 9x_4 \leq 365$
21. $10x_1 + 6x_2 \leq 316$
22. $x_3 + 9x_4 \leq 339$
23. $10x_1 + 6x_2 + 9x_4 \leq 435$
24. $6x_2 + x_3 + 9x_4 \leq 310$

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B4'),
        ('x2', 'milligrams of iron'),
        ('x3', 'milligrams of vitamin B3'),
        ('x4', 'milligrams of calcium')
    ],
    'objective_function': '8*x1 + 5*x2 + 3*x3 + 6*x4',
    'constraints': [
        '10*x1 + x3 >= 88',
        '6*x2 + x3 >= 45',
        '10*x1 + 6*x2 >= 104',
        '6*x2 + 9*x4 >= 124',
        '10*x1 + 6*x2 + 9*x4 >= 88',
        '10*x1 + 6*x2 + x3 >= 88',
        '10*x1 + x3 + 9*x4 >= 88',
        '10*x1 + 6*x2 + 9*x4 >= 106',
        '10*x1 + 6*x2 + x3 >= 106',
        '10*x1 + x3 + 9*x4 >= 106',
        '10*x1 + 6*x2 + 9*x4 >= 81',
        '10*x1 + 6*x2 + x3 >= 81',
        '10*x1 + x3 + 9*x4 >= 81',
        '10*x1 + 6*x2 + x3 + 9*x4 >= 81',
        '-2*x2 + 2*x3 >= 0',
        '10*x1 + 9*x4 <= 365',
        '10*x1 + 6*x2 <= 316',
        'x3 + 9*x4 <= 339',
        '10*x1 + 6*x2 + 9*x4 <= 435',
        '6*x2 + x3 + 9*x4 <= 310'
    ]
}
```

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

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

    # Define variables
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B4
    x2 = model.addVar(name="x2")  # milligrams of iron
    x3 = model.addVar(name="x3")  # milligrams of vitamin B3
    x4 = model.addVar(name="x4")  # milligrams of calcium

    # Objective function
    model.setObjective(8 * x1 + 5 * x2 + 3 * x3 + 6 * x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * x1 + x3 >= 88)
    model.addConstr(6 * x2 + x3 >= 45)
    model.addConstr(10 * x1 + 6 * x2 >= 104)
    model.addConstr(6 * x2 + 9 * x4 >= 124)
    model.addConstr(10 * x1 + 6 * x2 + 9 * x4 >= 88)
    model.addConstr(10 * x1 + 6 * x2 + x3 >= 88)
    model.addConstr(10 * x1 + x3 + 9 * x4 >= 88)
    model.addConstr(10 * x1 + 6 * x2 + 9 * x4 >= 106)
    model.addConstr(10 * x1 + 6 * x2 + x3 >= 106)
    model.addConstr(10 * x1 + x3 + 9 * x4 >= 106)
    model.addConstr(10 * x1 + 6 * x2 + 9 * x4 >= 81)
    model.addConstr(10 * x1 + 6 * x2 + x3 >= 81)
    model.addConstr(10 * x1 + x3 + 9 * x4 >= 81)
    model.addConstr(10 * x1 + 6 * x2 + x3 + 9 * x4 >= 81)
    model.addConstr(-2 * x2 + 2 * x3 >= 0)
    model.addConstr(10 * x1 + 9 * x4 <= 365)
    model.addConstr(10 * x1 + 6 * x2 <= 316)
    model.addConstr(x3 + 9 * x4 <= 339)
    model.addConstr(10 * x1 + 6 * x2 + 9 * x4 <= 435)
    model.addConstr(6 * x2 + x3 + 9 * x4 <= 310)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"x1: {x1.varValue}")
        print(f"x2: {x2.varValue}")
        print(f"x3: {x3.varValue}")
        print(f"x4: {x4.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```