## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of flight jackets produced per day
- $x_2$ as the number of denim jackets produced per day

The objective is to maximize profit. The profit from $x_1$ flight jackets is $70x_1$ and from $x_2$ denim jackets is $100x_2$. Therefore, the objective function to maximize is $70x_1 + 100x_2$.

## Step 2: Identify the constraints

1. The flight jackets team can produce at most 10 flight jackets per day: $x_1 \leq 10$
2. The denim jackets team can produce at most 25 denim jackets per day: $x_2 \leq 25$
3. The sewing machine can process at most 30 jackets per day: $x_1 + x_2 \leq 30$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 3: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'flight jackets'), ('x2', 'denim jackets')],
    'objective_function': '70*x1 + 100*x2',
    'constraints': [
        'x1 <= 10',
        'x2 <= 25',
        'x1 + x2 <= 30',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Convert the problem into Gurobi code

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(lb=0, ub=10, name="flight_jackets")
x2 = model.addVar(lb=0, ub=25, name="denim_jackets")

# Set the objective function
model.setObjective(70*x1 + 100*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 <= 10, name="flight_jacket_limit")
model.addConstr(x2 <= 25, name="denim_jacket_limit")
model.addConstr(x1 + x2 <= 30, name="sewing_machine_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Flight jackets: {x1.varValue}")
    print(f"Denim jackets: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found.")
```