```json
{
  "sym_variables": [
    ("x1", "number of sofas"),
    ("x2", "number of beds")
  ],
  "objective_function": "100*x1 + 200*x2",
  "constraints": [
    "8*x1 + 12*x2 <= 500",
    "200*x1 + 300*x2 <= 12500",
    "x1 >= 0.3*(x1 + x2)",
    "x1 >= 0",
    "x2 >= 0"
  ]
}
```

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

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

# Create variables
sofas = m.addVar(lb=0, vtype=GRB.INTEGER, name="sofas")
beds = m.addVar(lb=0, vtype=GRB.INTEGER, name="beds")

# Set objective function
m.setObjective(100 * sofas + 200 * beds, GRB.MAXIMIZE)

# Add constraints
m.addConstr(8 * sofas + 12 * beds <= 500, "space_constraint")
m.addConstr(200 * sofas + 300 * beds <= 12500, "budget_constraint")
m.addConstr(sofas >= 0.3 * (sofas + beds), "sofa_proportion_constraint")


# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of Sofas: {sofas.x}")
    print(f"Number of Beds: {beds.x}")
    print(f"Maximum Profit: ${m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
