## 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 regular speakers made
- $x_2$ represents the number of portable speakers made

The objective is to maximize profit. The profit per regular speaker is $40, and the profit per portable speaker is $60. Therefore, the objective function can be represented as:

Maximize $40x_1 + 60x_2$

The constraints based on the given information are:
- Team A can make at most 120 regular speakers per day: $x_1 \leq 120$
- Team B can make at most 200 portable speakers per day: $x_2 \leq 200$
- The shared testing machine can be used to make a maximum of 300 total speakers per day: $x_1 + x_2 \leq 300$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'regular speakers'), ('x2', 'portable speakers')],
    'objective_function': '40*x1 + 60*x2',
    'constraints': [
        'x1 <= 120',
        'x2 <= 200',
        'x1 + x2 <= 300',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(lb=0, ub=120, name="regular_speakers")
x2 = model.addVar(lb=0, ub=200, name="portable_speakers")

# Objective function: Maximize profit
model.setObjective(40*x1 + 60*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 <= 120, name="team_a_capacity")
model.addConstr(x2 <= 200, name="team_b_capacity")
model.addConstr(x1 + x2 <= 300, name="testing_machine_capacity")

# Solve the model
model.optimize()

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