## Step 1: Define the symbolic variables and their corresponding natural language objects.
The symbolic variables and their corresponding natural language objects are:
- $x_0$ : milligrams of vitamin B3
- $x_1$ : milligrams of vitamin K
- $x_2$ : milligrams of vitamin B1
- $x_3$ : milligrams of calcium
- $x_4$ : milligrams of vitamin A
- $x_5$ : milligrams of iron

## Step 2: Formulate the objective function using the symbolic variables.
The objective function to minimize is: $7x_0 + x_1 + 2x_2 + 3x_3 + 5x_4 + 9x_5$

## 3: List the semi-algebraic constraints.
The constraints are:
- $x_0 \geq 0$ (Implicit, as there's no lower bound given)
- $x_1 \geq 0$ (Implicit, as there's no lower bound given)
- $x_2 \geq 0$ (Implicit, as there's no lower bound given)
- $x_3 \geq 0$ (Implicit, as there's no lower bound given)
- $x_4 \geq 0$ (Implicit, as there's no lower bound given)
- $x_5 \geq 0$ (Implicit, as there's no lower bound given)
- $5x_0 \leq 255$
- $12x_0 \leq 463$
- $14x_1 \leq 255$
- $2x_1 \leq 463$
- $17x_2 \leq 255$
- $10x_2 \leq 463$
- $14x_3 \leq 255$
- $3x_3 \leq 463$
- $2x_4 \leq 255$
- $3x_4 \leq 463$
- $x_5 \leq 255$
- $9x_5 \leq 463$
- $17x_2 + x_5 \geq 31$
- $14x_1 + x_5 \geq 29$
- $14x_3 + x_5 \geq 20$
- $14x_1 + 2x_4 \geq 36$
- $5x_0 + 14x_1 + 17x_2 + 14x_3 + 2x_4 + x_5 \geq 36$
- $3x_4 + 9x_5 \geq 75$
- $12x_0 + 2x_1 \geq 33$
- $12x_0 + 2x_1 + 10x_2 \geq 69$
- $12x_0 + 2x_1 + 10x_2 + 3x_3 + 3x_4 + 9x_5 \geq 69$
- $10x_0 - x_5 \geq 0$
- $17x_2 + x_5 \leq 206$
- $17x_2 + 14x_3 \leq 181$
- $14x_3 + x_5 \leq 46$
- $12x_0 + 3x_3 \leq 317$
- $10x_2 + 3x_3 \leq 96$
- $12x_0 + 2x_1 + 10x_2 \leq 248$
- $2x_1 + 10x_2 + 3x_4 \leq 420$
- $2x_1 + 3x_3 + 3x_4 \leq 147$
- $12x_0 + 2x_1 + 3x_4 \leq 234$
- $12x_0 + 3x_3 + 9x_5 \leq 168$
- $10x_2 + 3x_4 + 9x_5 \leq 366$
- $3x_3 + 3x_4 + 9x_5 \leq 196$
- $12x_0 + 10x_2 + 3x_4 \leq 384$
- $12x_0 + 2x_1 + 9x_5 \leq 259$
- $12x_0 + 10x_2 + 9x_5 \leq 130$
- $12x_0 + 2x_1 + 3x_3 \leq 210$
- $12x_0 + 3x_3 + 3x_4 \leq 254$
- $2x_1 + 10x_2 + 3x_3 \leq 382$
- $12x_0 + 10x_2 + 3x_3 \leq 106$

## 4: Represent the problem in JSON format.
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B3'),
        ('x1', 'milligrams of vitamin K'),
        ('x2', 'milligrams of vitamin B1'),
        ('x3', 'milligrams of calcium'),
        ('x4', 'milligrams of vitamin A'),
        ('x5', 'milligrams of iron')
    ],
    'objective_function': '7*x0 + x1 + 2*x2 + 3*x3 + 5*x4 + 9*x5',
    'constraints': [
        '5*x0 <= 255',
        '12*x0 <= 463',
        '14*x1 <= 255',
        '2*x1 <= 463',
        '17*x2 <= 255',
        '10*x2 <= 463',
        '14*x3 <= 255',
        '3*x3 <= 463',
        '2*x4 <= 255',
        '3*x4 <= 463',
        'x5 <= 255',
        '9*x5 <= 463',
        '17*x2 + x5 >= 31',
        '14*x1 + x5 >= 29',
        '14*x3 + x5 >= 20',
        '14*x1 + 2*x4 >= 36',
        '5*x0 + 14*x1 + 17*x2 + 14*x3 + 2*x4 + x5 >= 36',
        '3*x4 + 9*x5 >= 75',
        '12*x0 + 2*x1 >= 33',
        '12*x0 + 2*x1 + 10*x2 >= 69',
        '12*x0 + 2*x1 + 10*x2 + 3*x3 + 3*x4 + 9*x5 >= 69',
        '10*x0 - x5 >= 0',
        '17*x2 + x5 <= 206',
        '17*x2 + 14*x3 <= 181',
        '14*x3 + x5 <= 46',
        '12*x0 + 3*x3 <= 317',
        '10*x2 + 3*x3 <= 96',
        '12*x0 + 2*x1 + 10*x2 <= 248',
        '2*x1 + 10*x2 + 3*x4 <= 420',
        '2*x1 + 3*x3 + 3*x4 <= 147',
        '12*x0 + 2*x1 + 3*x4 <= 234',
        '12*x0 + 3*x3 + 9*x5 <= 168',
        '10*x2 + 3*x4 + 9*x5 <= 366',
        '3*x3 + 3*x4 + 9*x5 <= 196',
        '12*x0 + 10*x2 + 3*x4 <= 384',
        '12*x0 + 2*x1 + 9*x5 <= 259',
        '12*x0 + 10*x2 + 9*x5 <= 130',
        '12*x0 + 2*x1 + 3*x3 <= 210',
        '12*x0 + 3*x3 + 3*x4 <= 254',
        '2*x1 + 10*x2 + 3*x3 <= 382',
        '12*x0 + 10*x2 + 3*x3 <= 106'
    ]
}
```

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

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

    # Define variables
    x0 = model.addVar(lb=0, name="x0")  # milligrams of vitamin B3
    x1 = model.addVar(lb=0, name="x1")  # milligrams of vitamin K
    x2 = model.addVar(lb=0, name="x2")  # milligrams of vitamin B1
    x3 = model.addVar(lb=0, name="x3")  # milligrams of calcium
    x4 = model.addVar(lb=0, name="x4")  # milligrams of vitamin A
    x5 = model.addVar(lb=0, name="x5")  # milligrams of iron

    # Objective function
    model.setObjective(7 * x0 + x1 + 2 * x2 + 3 * x3 + 5 * x4 + 9 * x5, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5 * x0 <= 255)
    model.addConstr(12 * x0 <= 463)
    model.addConstr(14 * x1 <= 255)
    model.addConstr(2 * x1 <= 463)
    model.addConstr(17 * x2 <= 255)
    model.addConstr(10 * x2 <= 463)
    model.addConstr(14 * x3 <= 255)
    model.addConstr(3 * x3 <= 463)
    model.addConstr(2 * x4 <= 255)
    model.addConstr(3 * x4 <= 463)
    model.addConstr(x5 <= 255)
    model.addConstr(9 * x5 <= 463)
    model.addConstr(17 * x2 + x5 >= 31)
    model.addConstr(14 * x1 + x5 >= 29)
    model.addConstr(14 * x3 + x5 >= 20)
    model.addConstr(14 * x1 + 2 * x4 >= 36)
    model.addConstr(5 * x0 + 14 * x1 + 17 * x2 + 14 * x3 + 2 * x4 + x5 >= 36)
    model.addConstr(3 * x4 + 9 * x5 >= 75)
    model.addConstr(12 * x0 + 2 * x1 >= 33)
    model.addConstr(12 * x0 + 2 * x1 + 10 * x2 >= 69)
    model.addConstr(12 * x0 + 2 * x1 + 10 * x2 + 3 * x3 + 3 * x4 + 9 * x5 >= 69)
    model.addConstr(10 * x0 - x5 >= 0)
    model.addConstr(17 * x2 + x5 <= 206)
    model.addConstr(17 * x2 + 14 * x3 <= 181)
    model.addConstr(14 * x3 + x5 <= 46)
    model.addConstr(12 * x0 + 3 * x3 <= 317)
    model.addConstr(10 * x2 + 3 * x3 <= 96)
    model.addConstr(12 * x0 + 2 * x1 + 10 * x2 <= 248)
    model.addConstr(2 * x1 + 10 * x2 + 3 * x4 <= 420)
    model.addConstr(2 * x1 + 3 * x3 + 3 * x4 <= 147)
    model.addConstr(12 * x0 + 2 * x1 + 3 * x4 <= 234)
    model.addConstr(12 * x0 + 3 * x3 + 9 * x5 <= 168)
    model.addConstr(10 * x2 + 3 * x4 + 9 * x5 <= 366)
    model.addConstr(3 * x3 + 3 * x4 + 9 * x5 <= 196)
    model.addConstr(12 * x0 + 10 * x2 + 3 * x4 <= 384)
    model.addConstr(12 * x0 + 2 * x1 + 9 * x5 <= 259)
    model.addConstr(12 * x0 + 10 * x2 + 9 * x5 <= 130)
    model.addConstr(12 * x0 + 2 * x1 + 3 * x3 <= 210)
    model.addConstr(12 * x0 + 3 * x3 + 3 * x4 <= 254)
    model.addConstr(2 * x1 + 10 * x2 + 3 * x3 <= 382)
    model.addConstr(12 * x0 + 10 * x2 + 3 * x3 <= 106)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
        print("x5: ", x5.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```