## Symbolic Representation

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

Let's define the variables:
- $x_1$ = number of cutting boards
- $x_2$ = number of chairs

The objective is to maximize profit. The profit per cutting board is $14, and the profit per chair is $25. Therefore, the objective function can be represented as:

Maximize: $14x_1 + 25x_2$

The constraints are:
1. Time constraint: Each cutting board takes 30 minutes, and each chair takes 70 minutes. The artist has 1500 minutes available in a week.
   - $30x_1 + 70x_2 \leq 1500$

2. Material constraint: The artist only has enough wood to make 40 items total.
   - $x_1 + x_2 \leq 40$

3. Non-negativity constraint: The number of cutting boards and chairs cannot be negative.
   - $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'cutting boards'), ('x2', 'chairs')],
    'objective_function': '14*x1 + 25*x2',
    'constraints': [
        '30*x1 + 70*x2 <= 1500',
        'x1 + x2 <= 40',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='cutting_boards', lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='chairs', lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function: Maximize 14*x1 + 25*x2
    model.setObjective(14*x1 + 25*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(30*x1 + 70*x2 <= 1500, name='time_constraint')
    model.addConstr(x1 + x2 <= 40, name='material_constraint')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Maximum profit: ${14*x1.x + 25*x2.x:.2f}")
    else:
        print("The model is infeasible.")

solve_optimization_problem()
```