## Problem Description and Formulation

Autumn Auto aims to advertise its new minivans and supercars to baby boomers and millennials through TV commercials on two channels: global news and talent shows. The objective is to minimize the cost of advertising while reaching at least 50 million baby boomers and 30 million millennials.

Let's define the decision variables:
- \(x_1\): Number of talent show ads
- \(x_2\): Number of global news ads

The cost of each ad type is given:
- Talent show ad: $80,000
- Global news ad: $30,000

The reach of each ad type is:
- Talent show ad: 5 million baby boomers, 20 million millennials
- Global news ad: 13 million baby boomers, 7 million millennials

The constraints are:
1. Reach at least 50 million baby boomers: \(5x_1 + 13x_2 \geq 50\)
2. Reach at least 30 million millennials: \(20x_1 + 7x_2 \geq 30\)
3. Non-negativity: \(x_1 \geq 0, x_2 \geq 0\)
4. Integer solutions: \(x_1, x_2\) are integers (though Gurobi can handle this, we focus on the LP relaxation first)

The objective function to minimize the total cost is:
\[80,000x_1 + 30,000x_2\]

## Gurobi Code

```python
import gurobi

def autumn_auto_advertising():
    # Create a new model
    model = gurobi.Model()

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

    # Objective function: Minimize cost
    model.setObjective(80000*x1 + 30000*x2, gurobi.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 solution
    if model.status == gurobi.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("No optimal solution found.")

if __name__ == "__main__":
    autumn_auto_advertising()
```