## Symbolic Representation

Let's denote:
- $x_1$ as the number of talent show ads
- $x_2$ as the number of global news ads

The objective is to minimize the total cost, which can be represented as $80,000x_1 + 30,000x_2$.

The constraints are:
- Reach at least 50 million baby boomers: $5x_1 + 13x_2 \geq 50$
- Reach at least 30 million millennials: $20x_1 + 7x_2 \geq 30$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Gurobi Code

To solve this problem using Gurobi in Python, we can use the following code:

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="talent_show_ads", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="global_news_ads", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: minimize cost
model.setObjective(80000*x1 + 30000*x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(5*x1 + 13*x2 >= 50, name="baby_boomers")
model.addConstr(20*x1 + 7*x2 >= 30, name="millennials")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Talent Show Ads: {x1.varValue}")
    print(f"Global News Ads: {x2.varValue}")
    print(f"Minimum Cost: ${model.objVal:.2f}")
else:
    print("The model is infeasible or unbounded.")
```

## Full Response

```json
{
    'sym_variables': [('x1', 'talent show ads'), ('x2', 'global news ads')],
    'objective_function': '80000x1 + 30000x2',
    'constraints': ['5x1 + 13x2 >= 50', '20x1 + 7x2 >= 30', 'x1 >= 0', 'x2 >= 0']
}
```

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="talent_show_ads", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="global_news_ads", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: minimize cost
model.setObjective(80000*x1 + 30000*x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(5*x1 + 13*x2 >= 50, name="baby_boomers")
model.addConstr(20*x1 + 7*x2 >= 30, name="millennials")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Talent Show Ads: {x1.varValue}")
    print(f"Global News Ads: {x2.varValue}")
    print(f"Minimum Cost: ${model.objVal:.2f}")
else:
    print("The model is infeasible or unbounded.")
```