## Symbolic Representation of the Problem

The problem can be converted into a symbolic representation as follows:

- Let $x_1$ be the number of cutting boards and $x_2$ be the number of knife handles.

## Objective Function and Constraints

The objective function to maximize profit is: $100x_1 + 250x_2$

The constraints based on the problem description are:
- $x_1 \leq 30$ (cutting boards limit)
- $x_2 \leq 50$ (knife handles limit)
- $5x_1 + 10x_2 \leq 200$ (total hours limit)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints)

## JSON Representation

```json
{
    'sym_variables': [('x1', 'cutting boards'), ('x2', 'knife handles')],
    'objective_function': '100*x1 + 250*x2',
    'constraints': [
        'x1 <= 30',
        'x2 <= 50',
        '5*x1 + 10*x2 <= 200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, ub=30, name="cutting_boards")
    x2 = model.addVar(lb=0, ub=50, name="knife_handles")

    # Set objective function
    model.setObjective(100 * x1 + 250 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 <= 30, name="cutting_boards_limit")
    model.addConstr(x2 <= 50, name="knife_handles_limit")
    model.addConstr(5 * x1 + 10 * x2 <= 200, name="total_hours_limit")

    # Optimize model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Cutting boards: {x1.varValue}")
        print(f"Knife handles: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```