To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of leather chairs made by Team A.
- $x_2$ as the number of mesh chairs made by Team B.

The objective function is to maximize profit. Given that the profit per leather chair is $150 and the profit per mesh chair is $100, the objective function can be represented algebraically as:

\[ \text{Maximize: } 150x_1 + 100x_2 \]

The constraints based on the problem description are:
1. Team A can make at most 20 leather chairs a day: $x_1 \leq 20$.
2. Team B can make at most 30 mesh chairs a day: $x_2 \leq 30$.
3. The quality check team can check at most 30 chairs of either type per day: $x_1 + x_2 \leq 30$.

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

Thus, the symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of leather chairs'), ('x2', 'number of mesh chairs')],
    'objective_function': '150*x1 + 100*x2',
    'constraints': ['x1 <= 20', 'x2 <= 30', 'x1 + x2 <= 30', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code in Python to solve this optimization problem:

```python
from gurobipy import *

# Create a new model
m = Model("Office_Chair_Problem")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="leather_chairs")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="mesh_chairs")

# Set the objective function
m.setObjective(150*x1 + 100*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 20, "Team_A_Capacity")
m.addConstr(x2 <= 30, "Team_B_Capacity")
m.addConstr(x1 + x2 <= 30, "Quality_Check_Capacity")

# Optimize the model
m.optimize()

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