To solve this optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables as follows:

- $x_1$: Number of tables produced
- $x_2$: Number of chairs produced

The objective function is to maximize profit. Given that each table brings in $1000 and each chair brings in $300, the objective function can be represented algebraically as:

Maximize: $1000x_1 + 300x_2$

The constraints based on the hours available for crafting and polishing are:

- Crafting hours constraint: $5x_1 + 2x_2 \leq 25$ (since each table requires 5 hours of crafting and each chair requires 2 hours, and there are a maximum of 25 crafting hours available)
- Polishing hours constraint: $2x_1 + x_2 \leq 15$ (since each table requires 2 hours of polishing and each chair requires 1 hour, and there are a maximum of 15 polishing hours available)

Additionally, since the number of tables and chairs cannot be negative, we have:

- Non-negativity constraints: $x_1 \geq 0$, $x_2 \geq 0$

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'Number of tables produced'), ('x2', 'Number of chairs produced')],
    'objective_function': '1000*x1 + 300*x2',
    'constraints': ['5*x1 + 2*x2 <= 25', '2*x1 + x2 <= 15', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we can use the following code:
```python
from gurobipy import *

# Create a new model
m = Model("Woodshop_Problem")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="tables", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="chairs", lb=0)

# Set objective function
m.setObjective(1000*x1 + 300*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 2*x2 <= 25, "crafting_hours")
m.addConstr(2*x1 + x2 <= 15, "polishing_hours")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Tables produced: {x1.x}")
    print(f"Chairs produced: {x2.x}")
    print(f"Max Profit: {m.objVal}")
else:
    print("No optimal solution found")
```