## Symbolic Representation

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

Let's denote:
- \(x_1\) as the number of violins produced
- \(x_2\) as the number of harps produced

The objective is to maximize profit. Given that the profit per violin is $200 and per harp is $350, the objective function can be written as:
\[ \text{Maximize:} \quad 200x_1 + 350x_2 \]

The constraints based on the given resources are:
- Woodworking time: \(6x_1 + 2x_2 \leq 100\)
- Assembling time: \(2.5x_1 + 10x_2 \leq 150\)
- Non-negativity constraints: \(x_1 \geq 0, x_2 \geq 0\)

## Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 'violins'), ('x2', 'harps')],
  'objective_function': '200*x1 + 350*x2',
  'constraints': [
    '6*x1 + 2*x2 <= 100',
    '2.5*x1 + 10*x2 <= 150',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_factory_production_problem():
    # Create a new model
    model = gp.Model("Factory_Production")

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

    # Objective function: Maximize profit
    model.setObjective(200*x1 + 350*x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6*x1 + 2*x2 <= 100, name="woodworking_time")
    model.addConstr(2.5*x1 + 10*x2 <= 150, name="assembling_time")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution: Violins = {x1.varValue}, Harps = {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_factory_production_problem()
```