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:

- $x_1$ represents the number of desk chairs produced.
- $x_2$ represents the number of garden chairs produced.

The profit on each desk chair is $100, and on each garden chair is $150. The cost to make a desk chair is $200, and a garden chair is $300. The total monthly demand for both types of chairs combined is at most 250 units, and the monthly manufacturing budget for chairs is $35,000.

The objective function, which we want to maximize, can be represented as:
\[ \text{Maximize: } 100x_1 + 150x_2 \]

This represents the total profit from selling $x_1$ desk chairs and $x_2$ garden chairs.

The constraints are as follows:

1. The total number of chairs produced does not exceed the demand limit:
\[ x_1 + x_2 \leq 250 \]

2. The total cost of producing the chairs does not exceed the manufacturing budget:
\[ 200x_1 + 300x_2 \leq 35000 \]

3. Non-negativity constraints, since we cannot produce a negative number of chairs:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Therefore, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of desk chairs'), ('x2', 'number of garden chairs')],
    'objective_function': '100*x1 + 150*x2',
    'constraints': ['x1 + x2 <= 250', '200*x1 + 300*x2 <= 35000', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="desk_chairs")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="garden_chairs")

# Set the objective function
m.setObjective(100*x1 + 150*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 250, "demand_limit")
m.addConstr(200*x1 + 300*x2 <= 35000, "budget_limit")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of desk chairs: {x1.x}")
    print(f"Number of garden chairs: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```