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

Let's denote:
- $x_1$ as the number of days to operate in the Indian ocean
- $x_2$ as the number of days to operate in the Arctic ocean

The objective is to minimize the cost: $6000x_1 + 9000x_2$

The constraints are:
- $3.4x_1 + 6x_2 \geq 20$ (fish constraint)
- $2.2x_1 + 5x_2 \geq 12$ (crab constraint)
- $1.5x_1 + 3x_2 \geq 10$ (shrimp constraint)
- $x_1, x_2 \geq 0$ (non-negativity constraint)

## Step 2: Convert the problem into a Gurobi-compatible format

We need to adjust the constraints to be in a standard form. Since Gurobi can handle the given constraints directly, we'll keep them as is.

## 3: Write down the symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'days in Indian ocean'), ('x2', 'days in Arctic ocean')],
    'objective_function': '6000*x1 + 9000*x2',
    'constraints': [
        '3.4*x1 + 6*x2 >= 20',
        '2.2*x1 + 5*x2 >= 12',
        '1.5*x1 + 3*x2 >= 10',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 4: Implement the problem in Gurobi Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name='x1', lb=0, ub=gurobi.GRB.INFINITY)  # days in Indian ocean
    x2 = model.addVar(name='x2', lb=0, ub=gurobi.GRB.INFINITY)  # days in Arctic ocean

    # Define objective function
    model.setObjective(6000*x1 + 9000*x2, gurobi.GRB.MINIMIZE)

    # Define constraints
    model.addConstr(3.4*x1 + 6*x2 >= 20, name='fish_constraint')
    model.addConstr(2.2*x1 + 5*x2 >= 12, name='crab_constraint')
    model.addConstr(1.5*x1 + 3*x2 >= 10, name='shrimp_constraint')

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("The model is infeasible")

solve_omega_seafood_problem()
```