## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ represents the number of desk lamps
- $x_2$ represents the number of chandeliers

The objective function to maximize profit is: $200x_1 + 500x_2$

The constraints based on the problem description are:
1. $x_1 \geq 40$ (at least 40 desk lamps)
2. $20x_1 + 60x_2 \leq 1500$ (manufacturing time constraint)
3. $x_1 + 15x_2 \leq 300$ (light bulb constraint)
4. $x_1, x_2 \geq 0$ (non-negativity constraint, as the number of lamps and chandeliers cannot be negative)

## Step 2: Convert the problem into a Gurobi-compatible format

We need to express the problem in a way that can be solved by Gurobi. This involves defining the variables, the objective function, and the constraints in a format that Gurobi can understand.

## 3: Write the Gurobi code

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(lb=0, name="desk_lamps")  # Number of desk lamps
x2 = model.addVar(lb=0, name="chandeliers")  # Number of chandeliers

# Objective function: Maximize 200x1 + 500x2
model.setObjective(200 * x1 + 500 * x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 >= 40, name="min_desk_lamps")  # At least 40 desk lamps
model.addConstr(20 * x1 + 60 * x2 <= 1500, name="manufacturing_time")  # Manufacturing time constraint
model.addConstr(x1 + 15 * x2 <= 300, name="light_bulbs")  # Light bulb constraint

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Desk lamps: {x1.varValue}")
    print(f"Chandeliers: {x2.varValue}")
    print(f"Max profit: {200 * x1.varValue + 500 * x2.varValue}")
else:
    print("No optimal solution found.")
```

## 4: Provide the symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'desk lamps'), ('x2', 'chandeliers')],
    'objective_function': '200x1 + 500x2',
    'constraints': [
        'x1 >= 40',
        '20x1 + 60x2 <= 1500',
        'x1 + 15x2 <= 300',
        'x1, x2 >= 0'
    ]
}
```

The final answer is: 
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(lb=0, name="desk_lamps")  # Number of desk lamps
x2 = model.addVar(lb=0, name="chandeliers")  # Number of chandeliers

# Objective function: Maximize 200x1 + 500x2
model.setObjective(200 * x1 + 500 * x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 >= 40, name="min_desk_lamps")  # At least 40 desk lamps
model.addConstr(20 * x1 + 60 * x2 <= 1500, name="manufacturing_time")  # Manufacturing time constraint
model.addConstr(x1 + 15 * x2 <= 300, name="light_bulbs")  # Light bulb constraint

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Desk lamps: {x1.varValue}")
    print(f"Chandeliers: {x2.varValue}")
    print(f"Max profit: {200 * x1.varValue + 500 * x2.varValue}")
else:
    print("No optimal solution found.")
```