## Problem Description and Symbolic Representation

The problem involves finding the optimal mixture of two bags, A and B, to minimize the cost while satisfying the protein and calcium requirements.

### Symbolic Variables
Let's define the symbolic variables as follows:
- $x_1$: Number of bags of type A
- $x_2$: Number of bags of type B

### Objective Function
The objective is to minimize the total cost. The cost of bag A is $3.50 per bag, and the cost of bag B is $2.50 per bag. Therefore, the objective function can be represented as:
\[ \text{Minimize:} \quad 3.50x_1 + 2.50x_2 \]

### Constraints
1. Protein requirement: The mixture must contain at least 30 units of protein. Bag A contains 3 units of protein per bag, and Bag B contains 4 units of protein per bag.
\[ 3x_1 + 4x_2 \geq 30 \]
2. Calcium requirement: The mixture must contain at least 35 units of calcium. Bag A contains 4 units of calcium per bag, and Bag B contains 2 units of calcium per bag.
\[ 4x_1 + 2x_2 \geq 35 \]
3. Non-negativity constraints: The number of bags cannot be negative.
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'Bag A'), ('x2', 'Bag B')],
    'objective_function': '3.50*x1 + 2.50*x2',
    'constraints': [
        '3*x1 + 4*x2 >= 30',
        '4*x1 + 2*x2 >= 35',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name='Bag_A', lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name='Bag_B', lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Minimize 3.50*x1 + 2.50*x2
    model.setObjective(3.50 * x1 + 2.50 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3 * x1 + 4 * x2 >= 30, name='protein_requirement')
    model.addConstr(4 * x1 + 2 * x2 >= 35, name='calcium_requirement')

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found.")
        print(f"Number of bags of type A: {x1.varValue}")
        print(f"Number of bags of type B: {x2.varValue}")
        print(f"Total cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_pet_store_mixture_problem()
```