## Step 1: Define the symbolic representation of the variables
The variables are 'bananas' and 'black beans', 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 maximize is $5.82x_1^2 + 3.1x_1x_2 + 2.57x_2^2 + 2.55x_1 + 9.79x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $12x_1 + 17x_2 \geq 54$
2. $8x_1 - 7x_2 \geq 0$
3. $12x_1 + 17x_2 \leq 91$
4. $12x_1 + 17x_2 \leq 91$ (This is a repeat of the previous constraint, so we consider it as one constraint)
5. $x_1$ can be fractional, $x_2$ must be an integer.

## 4: Determine the bounds for calcium from the resources
Given that $r0$ represents milligrams of calcium with an upper bound of 128, but specific bounds from the problem statement are:
- Lower bound: $12x_1 + 17x_2 \geq 54$
- Upper bound: $12x_1 + 17x_2 \leq 91$

## 5: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'bananas'), ('x2', 'black beans')],
'objective_function': '5.82*x1^2 + 3.1*x1*x2 + 2.57*x2^2 + 2.55*x1 + 9.79*x2',
'constraints': [
    '12*x1 + 17*x2 >= 54',
    '8*x1 - 7*x2 >= 0',
    '12*x1 + 17*x2 <= 91'
]
}
```

## 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define variables
    bananas = model.addVar(name="bananas", lb=0, ub=None)
    black_beans = model.addVar(name="black beans", lb=0, integer=True)

    # Objective function
    model.setObjective(5.82 * bananas**2 + 3.1 * bananas * black_beans + 2.57 * black_beans**2 + 2.55 * bananas + 9.79 * black_beans, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(12 * bananas + 17 * black_beans >= 54, name="calcium_lower_bound")
    model.addConstr(8 * bananas - 7 * black_beans >= 0, name="bananas_vs_black_beans")
    model.addConstr(12 * bananas + 17 * black_beans <= 91, name="calcium_upper_bound")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Bananas: {bananas.varValue}")
        print(f"Black Beans: {black_beans.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```