## Symbolic Representation

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

Let's define the symbolic variables as follows:

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

The objective 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 as:

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 quality check at most 30 chairs of either type per day: $x_1 + x_2 \leq 30$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

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

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="leather_chairs", lb=0, ub=20, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="mesh_chairs", lb=0, ub=30, vtype=gp.GRB.INTEGER)

# Define the objective function
model.setObjective(150 * x1 + 100 * x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 <= 20, name="leather_chairs_limit")
model.addConstr(x2 <= 30, name="mesh_chairs_limit")
model.addConstr(x1 + x2 <= 30, name="quality_check_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {model.x[0].varName} = {model.x[0].x}, {model.x[1].varName} = {model.x[1].x}")
    print(f"Max Profit: ${150*model.x[0].x + 100*model.x[1].x:.2f}")
else:
    print("No optimal solution found.")
```