To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of interest (desk lamps and chandeliers), formulating the objective function based on the profit per item, and expressing the constraints related to manufacturing time and light bulbs.

Let's define:
- \(x_1\) as the number of desk lamps produced,
- \(x_2\) as the number of chandeliers produced.

The objective function aims to maximize profit. Given that each desk lamp yields a profit of $200 and each chandelier yields a profit of $500, the objective function can be written as:
\[ \text{Maximize} \quad 200x_1 + 500x_2 \]

The constraints are as follows:
1. Manufacturing time constraint: Each desk lamp takes 20 minutes, and each chandelier takes 60 minutes. The total available manufacturing time is 1500 minutes.
\[ 20x_1 + 60x_2 \leq 1500 \]
2. Light bulb constraint: Each desk lamp requires 1 light bulb, and each chandelier requires 15 light bulbs. There are 300 light bulbs available.
\[ x_1 + 15x_2 \leq 300 \]
3. Minimum production of desk lamps: The company must make at least 40 desk lamps.
\[ x_1 \geq 40 \]
4. Non-negativity constraints: The number of items produced cannot be negative.
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of desk lamps'), ('x2', 'number of chandeliers')],
    'objective_function': '200*x1 + 500*x2',
    'constraints': [
        '20*x1 + 60*x2 <= 1500',
        'x1 + 15*x2 <= 300',
        'x1 >= 40',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's write the Gurobi code in Python to solve this optimization problem:
```python
from gurobipy import *

# Create a model
m = Model("Lighting_Company_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="desk_lamps")
x2 = m.addVar(vtype=GRB.INTEGER, name="chandeliers")

# Set objective function
m.setObjective(200*x1 + 500*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 60*x2 <= 1500, "manufacturing_time")
m.addConstr(x1 + 15*x2 <= 300, "light_bulbs")
m.addConstr(x1 >= 40, "minimum_desk_lamps")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```