## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the profit of a violin factory by determining the optimal number of modern and baroque violins to produce given the available woodworking and assembling times.

Let's define the decision variables:
- \(x\): The number of modern violins to produce.
- \(y\): The number of baroque violins to produce.

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 150x + 200y \]

Subject to the constraints:
1. Woodworking time constraint: \( 5x + 4y \leq 150 \)
2. Assembling time constraint: \( 3.5x + 5y \leq 200 \)
3. Non-negativity constraints: \( x \geq 0, y \geq 0 \)

## Gurobi Code

To solve this problem using Gurobi in Python, we will use the Gurobi Python API. First, ensure you have Gurobi installed in your Python environment. You can install it via pip if you have the Gurobi license and the Gurobi software installed on your machine.

```python
import gurobi

def solve_violin_factory_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x = model.addVar(lb=0, name="modern_violins")  # Number of modern violins
    y = model.addVar(lb=0, name="baroque_violins")  # Number of baroque violins

    # Objective function: Maximize profit
    model.setObjective(150*x + 200*y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x + 4*y <= 150, name="woodworking_time")  # Woodworking time constraint
    model.addConstr(3.5*x + 5*y <= 200, name="assembling_time")  # Assembling time constraint

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found. Produce {x.varValue} modern violins and {y.varValue} baroque violins.")
        print(f"Maximum profit: ${150*x.varValue + 200*y.varValue:.2f}")
    else:
        print("No optimal solution found.")

# Run the function
solve_violin_factory_problem()
```