## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables:
- $x_1$ represents the number of scarfs
- $x_2$ represents the number of toques

The objective is to maximize profit. Given that the profit per scarf is $20 and the profit per toque is $25, the objective function can be written as:

Maximize: $20x_1 + 25x_2$

The factory has the following constraints:
- The factory has 250000 knitting minutes available. A scarf takes 20 minutes to knit and a toque takes 30 minutes to knit. This can be represented as:
  $20x_1 + 30x_2 \leq 250000$
- The factory must make at least 5000 scarfs: $x_1 \geq 5000$
- The factory must make at least 3000 toques: $x_2 \geq 3000$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'scarfs'), ('x2', 'toques')], 
    'objective_function': '20*x1 + 25*x2', 
    'constraints': [
        '20*x1 + 30*x2 <= 250000', 
        'x1 >= 5000', 
        'x2 >= 3000'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="scarfs", lb=0, vtype=gp.GRB.INTEGER)  # Number of scarfs
x2 = model.addVar(name="toques", lb=0, vtype=gp.GRB.INTEGER)  # Number of toques

# Objective function: Maximize profit
model.setObjective(20*x1 + 25*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(20*x1 + 30*x2 <= 250000, name="knitting_minutes")
model.addConstr(x1 >= 5000, name="min_scarfs")
model.addConstr(x2 >= 3000, name="min_toques")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {model.x[0]} scarfs, {model.x[1]} toques")
    print(f"Max profit: ${20*model.x[0] + 25*model.x[1]}")
else:
    print("No optimal solution found")
```