## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of laptop bags
- $x_2$ as the number of briefcases

The objective is to maximize profit, where the profit per laptop bag is $80 and per briefcase is $50. Therefore, the objective function is $80x_1 + 50x_2$.

## Step 2: Define the constraints based on the given resources

- Each laptop bag requires 12 minutes of sewing, and each briefcase requires 10 minutes of sewing. There are 300 minutes available for sewing. This gives us the constraint $12x_1 + 10x_2 \leq 300$.
- Each laptop bag requires 5 minutes of painting, and each briefcase requires 9 minutes of painting. There are 500 minutes available for painting. This gives us the constraint $5x_1 + 9x_2 \leq 500$.
- Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of bags cannot be negative.

## 3: Symbolic representation of the optimization problem

```json
{
    'sym_variables': [('x1', 'laptop bags'), ('x2', 'briefcases')],
    'objective_function': '80*x1 + 50*x2',
    'constraints': [
        '12*x1 + 10*x2 <= 300',
        '5*x1 + 9*x2 <= 500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Translate the symbolic representation into Gurobi code

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="laptop_bags", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="briefcases", lb=0, ub=gurobi.GRB.INFINITY)

    # Objective function: maximize 80*x1 + 50*x2
    model.setObjective(80*x1 + 50*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(12*x1 + 10*x2 <= 300, name="sewing_time")
    model.addConstr(5*x1 + 9*x2 <= 500, name="painting_time")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: laptop bags = {x1.varValue}, briefcases = {x2.varValue}")
    else:
        print("No optimal solution found")

solve_bag_production()
```