To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- \(x_1\) as the number of bags of berry mix A purchased,
- \(x_2\) as the number of bags of berry mix B purchased.

The objective is to minimize the total cost. Given that berry mix A costs $5 per bag and berry mix B costs $3 per bag, the objective function can be represented algebraically as:
\[ \text{Minimize:} \quad 5x_1 + 3x_2 \]

The constraints are based on the requirements for blueberries and blackberries:
- At least 150 g of blueberries: \(30x_1 + 20x_2 \geq 150\)
- At least 125 g of blackberries: \(45x_1 + 15x_2 \geq 125\)

Additionally, we should consider non-negativity constraints since the number of bags cannot be negative:
- \(x_1 \geq 0\)
- \(x_2 \geq 0\)

Thus, the symbolic representation of the problem in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of bags of berry mix A'), ('x2', 'number of bags of berry mix B')],
    'objective_function': '5*x1 + 3*x2',
    'constraints': ['30*x1 + 20*x2 >= 150', '45*x1 + 15*x2 >= 125', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Berry_Mix_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="berry_mix_A", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="berry_mix_B", lb=0)

# Set the objective function
m.setObjective(5*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(30*x1 + 20*x2 >= 150, "blueberries_constraint")
m.addConstr(45*x1 + 15*x2 >= 125, "blackberries_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of bags of Berry Mix A: {x1.x}")
    print(f"Number of bags of Berry Mix B: {x2.x}")
    print(f"Total cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found.")
```