## Step 1: Define the symbolic representation of the variables
The variables are 'pickles' and 'cantaloupes', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5x_1^2 + 2x_1x_2 + 5x_2^2 + 2x_1 + 2x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $5x_1 + 11x_2 \geq 24$ (calcium from pickles and cantaloupes)
- $5x_1 \geq 24$ (calcium from pickles)
- $10x_1 + 4x_2 \geq 9$ (sourness index from pickles and cantaloupes)
- $3x_1 - 6x_2 \geq 0$ (relationship between pickles and cantaloupes)
- $5x_1 + 11x_2 \leq 76$ (maximum calcium from pickles and cantaloupes)
- $10^2x_1^2 + 4^2x_2^2 \leq 32$ (sourness index squared constraint)
- $4x_1 + x_2 \geq 25$ (minimum cost)
- $4x_1 + x_2 \leq 48$ (maximum cost)
- $x_1$ is an integer (nonfractional number of pickles)
- $x_2$ can be a real number (possibly non-whole number of cantaloupes)

## 4: Correct and Simplify Constraints for Accuracy
Correcting and simplifying the constraints for accuracy:
- The constraint for calcium from both is $5x_1 + 11x_2 \geq 24$.
- The constraint for calcium from pickles alone is $5x_1 \geq 24$.
- The sourness index constraint is $10x_1 + 4x_2 \geq 9$.
- The relationship constraint is $3x_1 - 6x_2 \geq 0$.
- The maximum calcium constraint is $5x_1 + 11x_2 \leq 76$.
- The sourness index squared constraint seems misinterpreted; correctly it should relate to $(10x_1)^2 + (4x_2)^2 \leq 32$ or simply $100x_1^2 + 16x_2^2 \leq 32$.
- The cost constraints are $4x_1 + x_2 \geq 25$ and $4x_1 + x_2 \leq 48$.

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'pickles'), ('x2', 'cantaloupes')],
'objective_function': '5*x1^2 + 2*x1*x2 + 5*x2^2 + 2*x1 + 2*x2',
'constraints': [
    '5*x1 + 11*x2 >= 24',
    '5*x1 >= 24',
    '10*x1 + 4*x2 >= 9',
    '3*x1 - 6*x2 >= 0',
    '5*x1 + 11*x2 <= 76',
    '100*x1^2 + 16*x2^2 <= 32',
    '4*x1 + x2 >= 25',
    '4*x1 + x2 <= 48',
    'x1 % 1 == 0'  # Ensuring x1 is an integer
]
}
```

## 6: Gurobi Code
Now, let's implement this in Gurobi:
```python
import gurobi

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

    # Define variables
    x1 = m.addVar(name="pickles", vtype=gurobi.GRB.INTEGER)  # Integer for pickles
    x2 = m.addVar(name="cantaloupes")  # Continuous for cantaloupes

    # Objective function
    m.setObjective(5*x1**2 + 2*x1*x2 + 5*x2**2 + 2*x1 + 2*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    m.addConstr(5*x1 + 11*x2 >= 24, name="calcium_min")
    m.addConstr(5*x1 >= 24, name="calcium_from_pickles_min")
    m.addConstr(10*x1 + 4*x2 >= 9, name="sourness_min")
    m.addConstr(3*x1 - 6*x2 >= 0, name="relationship")
    m.addConstr(5*x1 + 11*x2 <= 76, name="calcium_max")
    m.addConstr(100*x1**2 + 16*x2**2 <= 32, name="sourness_squared_max")
    m.addConstr(4*x1 + x2 >= 25, name="cost_min")
    m.addConstr(4*x1 + x2 <= 48, name="cost_max")

    # Optimize
    m.optimize()

    # Print solution
    if m.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", m.objVal)
        print("Pickles: ", x1.varValue)
        print("Cantaloupes: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```