## Symbolic Representation

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

Let's define the symbolic variables as follows:

- $x_1$ represents the number of bedside tables produced.
- $x_2$ represents the number of bookcases produced.

The objective is to maximize profit. The profit from the sale of each bedside table is $200, and the profit from the sale of each bookcase is $500. Therefore, the objective function can be represented as:

Maximize $200x_1 + 500x_2$

The constraints based on the given information are:

1. Crafting hours: $2.5x_1 + 5x_2 \leq 30$
2. Polishing hours: $1.5x_1 + 3x_2 \leq 20$
3. Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bedside tables'), ('x2', 'bookcases')],
    'objective_function': '200*x1 + 500*x2',
    'constraints': [
        '2.5*x1 + 5*x2 <= 30',
        '1.5*x1 + 3*x2 <= 20',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Furniture_Factory_Optimization")

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

# Define the objective function
model.setObjective(200*x1 + 500*x2, gp.GRB.MAXIMIZE)

# Add the constraints
model.addConstr(2.5*x1 + 5*x2 <= 30, name="crafting_hours")
model.addConstr(1.5*x1 + 3*x2 <= 20, name="polishing_hours")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found: x1 = {x1.varValue}, x2 = {x2.varValue}")
    print(f"Maximum profit: ${200*x1.varValue + 500*x2.varValue:.2f}")
else:
    print("No optimal solution found.")
```