```json
{
  "sym_variables": [
    ("x1", "number of billboard ads"),
    ("x2", "number of podcast ads"),
    ("x3", "number of merchandise ads")
  ],
  "objective_function": "40000*x1 + 10000*x2 + 2000*x3",
  "constraints": [
    "750*x1 + 1000*x2 + 300*x3 <= 20000",
    "x1 <= 3",
    "x3 <= 0.4*(x1 + x2 + x3)",
    "x2 >= 0.25*(x1 + x2 + x3)",
    "x1 >= 0",
    "x2 >= 0",
    "x3 >= 0"
  ]
}
```

```python
from gurobipy import Model, GRB

# Create a new model
model = Model("Maximus_Advertising")

# Create variables
billboard_ads = model.addVar(vtype=GRB.INTEGER, name="billboard_ads")
podcast_ads = model.addVar(vtype=GRB.INTEGER, name="podcast_ads")
merchandise_ads = model.addVar(vtype=GRB.INTEGER, name="merchandise_ads")

# Set objective function
model.setObjective(40000 * billboard_ads + 10000 * podcast_ads + 2000 * merchandise_ads, GRB.MAXIMIZE)

# Add constraints
model.addConstr(750 * billboard_ads + 1000 * podcast_ads + 300 * merchandise_ads <= 20000, "budget_constraint")
model.addConstr(billboard_ads <= 3, "billboard_limit")
model.addConstr(merchandise_ads <= 0.4 * (billboard_ads + podcast_ads + merchandise_ads), "merchandise_proportion")
model.addConstr(podcast_ads >= 0.25 * (billboard_ads + podcast_ads + merchandise_ads), "podcast_proportion")


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Viewership: {model.objVal}")
    print(f"Number of Billboard Ads: {billboard_ads.x}")
    print(f"Number of Podcast Ads: {podcast_ads.x}")
    print(f"Number of Merchandise Ads: {merchandise_ads.x}")
elif model.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {model.status}")

```
