## Problem Description and Formulation

Avian cosmetics aims to advertise its luxury beauty products through commercials on concerts and cinema programs. The goal is to minimize the cost of advertising while ensuring that the commercials are seen by at least 86 million young girls and 72 million middle-aged women.

### Decision Variables

Let:
- \(x_c\) be the number of 1-minute commercials on concerts,
- \(x_{cin}\) be the number of 1-minute commercials on cinema.

### Objective Function

The objective is to minimize the total cost of advertising, given by:
\[ \text{Minimize:} \quad 80,000x_c + 30,000x_{cin} \]

### Constraints

1. **Young Girls Constraint:** The total number of young girls seeing the commercials must be at least 86 million.
\[ 9x_c + 5x_{cin} \geq 86,000,000 \]

2. **Middle-aged Women Constraint:** The total number of middle-aged women seeing the commercials must be at least 72 million.
\[ 4x_c + 45x_{cin} \geq 72,000,000 \]

3. **Non-Negativity Constraints:** The number of commercials cannot be negative.
\[ x_c \geq 0, \quad x_{cin} \geq 0 \]

## Gurobi Code

```python
import gurobi

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

    # Define decision variables
    x_c = model.addVar(name="concert_commercials", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x_cin = model.addVar(name="cinema_commercials", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Minimize cost
    model.setObjective(80000*x_c + 30000*x_cin, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(9*x_c + 5*x_cin >= 86000000, name="young_girls_constraint")
    model.addConstr(4*x_c + 45*x_cin >= 72000000, name="middle_aged_women_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Concert Commercials: {x_c.varValue}")
        print(f"Cinema Commercials: {x_cin.varValue}")
        print(f"Total Cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

# Run the model
avian_cosmetics_advertising()
```