## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and the objective function based on the given problem description.

- Let $x_0$ represent 'green beans', $x_1$ represent 'oranges', and $x_2$ represent 'slices of pizza'.

## Step 2: Translate the objective function into algebraic terms
The objective function to minimize is: $3.42x_0x_1 + 7.77x_1x_2 + 6.09x_2^2 + 3.32x_0 + 2.66x_1$.

## 3: List all constraints in algebraic terms
1. $4x_0 + 16x_1 + 20x_2 \leq 107$ (total cost constraint)
2. $5x_0 + 16x_1 + 7x_2 \leq 113$ (total tastiness rating constraint)
3. $x_0^2 + x_2^2 \geq 21$ (green beans and slices of pizza cost constraint)
4. $x_1^2 + x_2^2 \geq 23$ (oranges and slices of pizza cost constraint)
5. $4x_0 + 16x_1 \geq 11$ (green beans and oranges cost constraint)
6. $4x_0 + 16x_1 + 20x_2 \geq 23$ (total cost constraint)
7. $5x_0 + 16x_1 \geq 37$ (green beans and oranges tastiness constraint)
8. $16x_1 + 7x_2 \geq 20$ (oranges and slices of pizza tastiness constraint)
9. $5x_0 + 16x_1 + 7x_2 \geq 25$ (total tastiness rating constraint)
10. $2x_0 - 10x_2 \geq 0$ (green beans and slices of pizza relationship constraint)
11. $5x_0 + 7x_2 \leq 68$ (green beans and slices of pizza tastiness constraint)
12. $16x_1^2 + 7x_2^2 \leq 99$ (oranges and slices of pizza tastiness squared constraint)
13. $x_0$ is an integer (green beans are whole numbers)
14. $x_2$ is an integer (slices of pizza are whole numbers)

## 4: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x0', 'green beans'), ('x1', 'oranges'), ('x2', 'slices of pizza')],
'objective_function': '3.42*x0*x1 + 7.77*x1*x2 + 6.09*x2^2 + 3.32*x0 + 2.66*x1',
'constraints': [
    '4*x0 + 16*x1 + 20*x2 <= 107',
    '5*x0 + 16*x1 + 7*x2 <= 113',
    'x0^2 + x2^2 >= 21',
    'x1^2 + x2^2 >= 23',
    '4*x0 + 16*x1 >= 11',
    '4*x0 + 16*x1 + 20*x2 >= 23',
    '5*x0 + 16*x1 >= 37',
    '16*x1 + 7*x2 >= 20',
    '5*x0 + 16*x1 + 7*x2 >= 25',
    '2*x0 - 10*x2 >= 0',
    '5*x0 + 7*x2 <= 68',
    '16*x1^2 + 7*x2^2 <= 99',
    'x0 == int(x0)',
    'x2 == int(x2)'
]
}
```

## 5: Gurobi Code
Now, let's write the Gurobi code to solve this optimization problem:
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name='green_beans', vtype=gurobi.GRB.INTEGER)  # green beans
    x1 = model.addVar(name='oranges', vtype=gurobi.GRB.CONTINUOUS)  # oranges
    x2 = model.addVar(name='slices_of_pizza', vtype=gurobi.GRB.INTEGER)  # slices of pizza

    # Objective function
    model.setObjective(3.42*x0*x1 + 7.77*x1*x2 + 6.09*x2**2 + 3.32*x0 + 2.66*x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4*x0 + 16*x1 + 20*x2 <= 107)  # total cost constraint
    model.addConstr(5*x0 + 16*x1 + 7*x2 <= 113)  # total tastiness rating constraint
    model.addConstr(x0**2 + x2**2 >= 21)  # green beans and slices of pizza cost constraint
    model.addConstr(x1**2 + x2**2 >= 23)  # oranges and slices of pizza cost constraint
    model.addConstr(4*x0 + 16*x1 >= 11)  # green beans and oranges cost constraint
    model.addConstr(4*x0 + 16*x1 + 20*x2 >= 23)  # total cost constraint
    model.addConstr(5*x0 + 16*x1 >= 37)  # green beans and oranges tastiness constraint
    model.addConstr(16*x1 + 7*x2 >= 20)  # oranges and slices of pizza tastiness constraint
    model.addConstr(5*x0 + 16*x1 + 7*x2 >= 25)  # total tastiness rating constraint
    model.addConstr(2*x0 - 10*x2 >= 0)  # green beans and slices of pizza relationship constraint
    model.addConstr(5*x0 + 7*x2 <= 68)  # green beans and slices of pizza tastiness constraint
    model.addConstr(16*x1**2 + 7*x2**2 <= 99)  # oranges and slices of pizza tastiness squared constraint

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Green beans: ', x0.varValue)
        print('Oranges: ', x1.varValue)
        print('Slices of pizza: ', x2.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```