## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_0$ represents 'milligrams of vitamin B3'
- $x_1$ represents 'milligrams of vitamin B7'
- $x_2$ represents 'milligrams of iron'

The objective function to maximize is $3x_0 + 9x_1 + 4x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $15x_0 \leq 180$
- $3x_0 \leq 379$
- $21x_0 \leq 379$
- $27x_1 \leq 180$
- $29x_1 \leq 379$
- $24x_1 \leq 379$
- $27x_2 \leq 180$
- $10x_2 \leq 379$
- $13x_2 \leq 379$
- $15x_0 + 27x_1 + 27x_2 \geq 53$
- $3x_0 + 10x_2 \geq 106$
- $29x_1 + 10x_2 \geq 118$
- $15x_0 + 27x_2 \leq 77$
- $15x_0 + 27x_1 + 27x_2 \leq 77$
- $3x_0 + 10x_2 \leq 146$
- $29x_1 + 10x_2 \leq 248$
- $3x_0 + 29x_1 + 10x_2 \leq 248$
- $21x_0 + 24x_1 \leq 209$
- $24x_1 + 13x_2 \leq 255$
- $21x_0 + 24x_1 + 13x_2 \leq 255$
- $x_0$ is an integer
- $x_1$ is continuous
- $x_2$ is an integer

## 3: Convert the problem into a Gurobi code
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi as gp

# Create a new model
model = gp.Model("optimization_problem")

# Define the variables
x0 = model.addVar(name="x0", vtype=gp.GRB.INTEGER)  # milligrams of vitamin B3
x1 = model.addVar(name="x1")  # milligrams of vitamin B7
x2 = model.addVar(name="x2", vtype=gp.GRB.INTEGER)  # milligrams of iron

# Define the objective function
model.setObjective(3*x0 + 9*x1 + 4*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(15*x0 <= 180, name="c1")
model.addConstr(3*x0 <= 379, name="c2")
model.addConstr(21*x0 <= 379, name="c3")
model.addConstr(27*x1 <= 180, name="c4")
model.addConstr(29*x1 <= 379, name="c5")
model.addConstr(24*x1 <= 379, name="c6")
model.addConstr(27*x2 <= 180, name="c7")
model.addConstr(10*x2 <= 379, name="c8")
model.addConstr(13*x2 <= 379, name="c9")
model.addConstr(15*x0 + 27*x1 + 27*x2 >= 53, name="c10")
model.addConstr(3*x0 + 10*x2 >= 106, name="c11")
model.addConstr(29*x1 + 10*x2 >= 118, name="c12")
model.addConstr(15*x0 + 27*x2 <= 77, name="c13")
model.addConstr(15*x0 + 27*x1 + 27*x2 <= 77, name="c14")
model.addConstr(3*x0 + 10*x2 <= 146, name="c15")
model.addConstr(29*x1 + 10*x2 <= 248, name="c16")
model.addConstr(3*x0 + 29*x1 + 10*x2 <= 248, name="c17")
model.addConstr(21*x0 + 24*x1 <= 209, name="c18")
model.addConstr(24*x1 + 13*x2 <= 255, name="c19")
model.addConstr(21*x0 + 24*x1 + 13*x2 <= 255, name="c20")

# Optimize the model
model.optimize()

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

## 4: Symbolic Representation
The symbolic representation of the problem is as follows:

```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B3'), 
        ('x1', 'milligrams of vitamin B7'), 
        ('x2', 'milligrams of iron')
    ], 
    'objective_function': '3*x0 + 9*x1 + 4*x2', 
    'constraints': [
        '15*x0 <= 180', 
        '3*x0 <= 379', 
        '21*x0 <= 379', 
        '27*x1 <= 180', 
        '29*x1 <= 379', 
        '24*x1 <= 379', 
        '27*x2 <= 180', 
        '10*x2 <= 379', 
        '13*x2 <= 379', 
        '15*x0 + 27*x1 + 27*x2 >= 53', 
        '3*x0 + 10*x2 >= 106', 
        '29*x1 + 10*x2 >= 118', 
        '15*x0 + 27*x2 <= 77', 
        '15*x0 + 27*x1 + 27*x2 <= 77', 
        '3*x0 + 10*x2 <= 146', 
        '29*x1 + 10*x2 <= 248', 
        '3*x0 + 29*x1 + 10*x2 <= 248', 
        '21*x0 + 24*x1 <= 209', 
        '24*x1 + 13*x2 <= 255', 
        '21*x0 + 24*x1 + 13*x2 <= 255'
    ]
}
```