## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = number of 1-minute concert ads
- $x_2$ = number of 1-minute cinema ads

The objective is to minimize the total cost. The cost of a 1-minute concert ad is $80,000, and the cost of a 1-minute cinema ad is $30,000. Therefore, the objective function can be represented as:

Minimize $80,000x_1 + 30,000x_2$

The constraints are:
- Each concert commercial is seen by 9 million young girls, and each cinema commercial is seen by 5 million young girls. Avian wants the commercials to be seen by at least 86 million young girls. This can be represented as:
$9x_1 + 5x_2 \geq 86$

- Each concert commercial is seen by 4 million middle-aged women, and each cinema commercial is seen by 45 million middle-aged women. Avian wants the commercials to be seen by at least 72 million middle-aged women. This can be represented as:
$4x_1 + 45x_2 \geq 72$

- Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of ads cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'number of 1-minute concert ads'), ('x2', 'number of 1-minute cinema ads')],
    'objective_function': '80000*x1 + 30000*x2',
    'constraints': [
        '9*x1 + 5*x2 >= 86',
        '4*x1 + 45*x2 >= 72',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="concert_ads", lb=0, vtype=gp.GRB.CONTINUOUS)  # number of 1-minute concert ads
x2 = model.addVar(name="cinema_ads", lb=0, vtype=gp.GRB.CONTINUOUS)  # number of 1-minute cinema ads

# Define the objective function
model.setObjective(80000*x1 + 30000*x2, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(9*x1 + 5*x2 >= 86, name="young_girls_constraint")
model.addConstr(4*x1 + 45*x2 >= 72, name="middle_aged_women_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Number of 1-minute concert ads: {x1.varValue}")
    print(f"Number of 1-minute cinema ads: {x2.varValue}")
    print(f"Minimum cost: ${model.objVal:.2f}")
else:
    print("The model is infeasible or unbounded.")
```