## Symbolic Representation

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

- \(x_1\) as the number of modern violins
- \(x_2\) as the number of baroque violins

The objective is to maximize profit. The profit per modern violin is $150, and the profit per baroque violin is $200. Therefore, the objective function can be represented as:

\[ \text{Maximize:} \quad 150x_1 + 200x_2 \]

The constraints based on the given resources are:

- Woodworking time: \(5x_1 + 4x_2 \leq 150\)
- Assembling time: \(3.5x_1 + 5x_2 \leq 200\)
- Non-negativity: \(x_1 \geq 0, x_2 \geq 0\)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'modern violin'), ('x2', 'baroque violin')],
    'objective_function': '150*x1 + 200*x2',
    'constraints': [
        '5*x1 + 4*x2 <= 150',
        '3.5*x1 + 5*x2 <= 200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="modern_violins", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="baroque_violins", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function: Maximize profit
model.setObjective(150*x1 + 200*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(5*x1 + 4*x2 <= 150, name="woodworking_time")
model.addConstr(3.5*x1 + 5*x2 <= 200, name="assembling_time")

# Solve the model
model.optimize()

# Print the results
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: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```