To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's define:
- $x_1$ as the number of folding bikes to stock.
- $x_2$ as the number of touring bikes to stock.

The profit from selling one folding bike is $200, and the profit from selling one touring bike is $350. Therefore, the objective function to maximize profit can be written as:
\[ \text{Maximize:} \quad 200x_1 + 350x_2 \]

The constraints given are:
1. The total number of bikes should not exceed 100.
2. The total value of bikes in stock should not exceed $30,000.

Given that the cost of a folding bike is $550 and a touring bike is $700, we can express these constraints as:
\[ x_1 + x_2 \leq 100 \] (Total number of bikes constraint)
\[ 550x_1 + 700x_2 \leq 30000 \] (Total value of bikes constraint)

Additionally, since the number of bikes cannot be negative, we have non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Now, let's represent this problem symbolically and in code format as requested:

```json
{
    'sym_variables': [('x1', 'number of folding bikes'), ('x2', 'number of touring bikes')],
    'objective_function': '200*x1 + 350*x2',
    'constraints': ['x1 + x2 <= 100', '550*x1 + 700*x2 <= 30000', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll write the following code:

```python
from gurobipy import *

# Create a model
m = Model("Bike_Stocking")

# Define variables
x1 = m.addVar(name='x1', lb=0)  # Number of folding bikes
x2 = m.addVar(name='x2', lb=0)  # Number of touring bikes

# Set the objective function
m.setObjective(200*x1 + 350*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, name='total_bikes')
m.addConstr(550*x1 + 700*x2 <= 30000, name='total_value')

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.x}, x2 = {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```