Here's how we can model this problem and generate the Gurobi code:

**Decision Variables:**

* `x`: Number of office chairs to stock.
* `y`: Number of dining chairs to stock.

**Objective Function:**

Maximize profit: `120x + 180y`

**Constraints:**

* **Budget Constraint:** `200x + 250y <= 20000`
* **Demand Constraint:** `x + y <= 130`
* **Non-negativity Constraints:** `x >= 0`, `y >= 0`


```python
import gurobipy as gp
from gurobipy import GRB

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

# Create decision variables
x = m.addVar(vtype=GRB.INTEGER, name="office_chairs")
y = m.addVar(vtype=GRB.INTEGER, name="dining_chairs")

# Set objective function
m.setObjective(120 * x + 180 * y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(200 * x + 250 * y <= 20000, "budget_constraint")
m.addConstr(x + y <= 130, "demand_constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of office chairs: {x.x}")
    print(f"Number of dining chairs: {y.x}")
    print(f"Maximum Profit: {m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
