## 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.

## Step 2: Identify the variables and their corresponding symbolic representations
The variables are 'strips of bacon', 'fruit salads', and 'ham sandwiches', which we can represent symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## 3: Translate the objective function into algebraic terms
The objective function to minimize is $2x_0^2 + 5x_0x_1 + x_1^2 + x_1x_2 + 9x_0 + 7x_1 + x_2$.

## 4: List the constraints in algebraic terms
The constraints are:
- $7x_0 \leq 97$
- $7x_0 \leq 69$
- $8x_0 \leq 66$
- $8x_1 \leq 97$
- $3x_1 \leq 69$
- $2x_1 \leq 66$
- $8x_2 \leq 97$
- $6x_2 \leq 69$
- $6x_2 \leq 66$
- $8x_1^2 + 8x_2^2 \geq 22$
- $7x_0 + 8x_2 \geq 22$
- $7x_0 + 8x_1 + 8x_2 \geq 22$
- $3x_1 + 6x_2 \geq 8$
- $7^2x_0^2 + 3^2x_1^2 \geq 20$
- $7x_0 + 3x_1 + 6x_2 \geq 20$
- $2x_1 + 6x_2 \geq 18$
- $8^2x_0^2 + 6^2x_2^2 \geq 20$
- $8x_0 + 2x_1 + 6x_2 \geq 22$
- $8x_0 + 2x_1 + 6x_2 \geq 22$
- $4x_1 - 5x_2 \geq 0$
- $10x_0^2 - 5x_2^2 \geq 0$
- $7x_0 + 8x_1 \leq 74$
- $8x_1 + 8x_2 \leq 75$
- $7x_0 + 6x_2 \leq 57$
- $7^2x_0^2 + 3^2x_1^2 + 6^2x_2^2 \leq 53$
- $x_0$ is an integer
- $x_2$ is an integer

## 5: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [
        ('x0', 'strips of bacon'), 
        ('x1', 'fruit salads'), 
        ('x2', 'ham sandwiches')
    ], 
    'objective_function': '2*x0^2 + 5*x0*x1 + x1^2 + x1*x2 + 9*x0 + 7*x1 + x2', 
    'constraints': [
        '7*x0 <= 97',
        '7*x0 <= 69',
        '8*x0 <= 66',
        '8*x1 <= 97',
        '3*x1 <= 69',
        '2*x1 <= 66',
        '8*x2 <= 97',
        '6*x2 <= 69',
        '6*x2 <= 66',
        '8*x1^2 + 8*x2^2 >= 22',
        '7*x0 + 8*x2 >= 22',
        '7*x0 + 8*x1 + 8*x2 >= 22',
        '3*x1 + 6*x2 >= 8',
        '49*x0^2 + 9*x1^2 >= 20',
        '7*x0 + 3*x1 + 6*x2 >= 20',
        '2*x1 + 6*x2 >= 18',
        '64*x0^2 + 36*x2^2 >= 20',
        '8*x0 + 2*x1 + 6*x2 >= 22',
        '8*x0 + 2*x1 + 6*x2 >= 22',
        '4*x1 - 5*x2 >= 0',
        '10*x0^2 - 5*x2^2 >= 0',
        '7*x0 + 8*x1 <= 74',
        '8*x1 + 8*x2 <= 75',
        '7*x0 + 6*x2 <= 57',
        '49*x0^2 + 9*x1^2 + 36*x2^2 <= 53'
    ]
}
```

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

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # strips of bacon
    x1 = model.addVar(name="x1")  # fruit salads
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # ham sandwiches

    # Objective function
    model.setObjective(2*x0**2 + 5*x0*x1 + x1**2 + x1*x2 + 9*x0 + 7*x1 + x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7*x0 <= 97)
    model.addConstr(7*x0 <= 69)
    model.addConstr(8*x0 <= 66)
    model.addConstr(8*x1 <= 97)
    model.addConstr(3*x1 <= 69)
    model.addConstr(2*x1 <= 66)
    model.addConstr(8*x2 <= 97)
    model.addConstr(6*x2 <= 69)
    model.addConstr(6*x2 <= 66)
    model.addConstr(8*x1**2 + 8*x2**2 >= 22)
    model.addConstr(7*x0 + 8*x2 >= 22)
    model.addConstr(7*x0 + 8*x1 + 8*x2 >= 22)
    model.addConstr(3*x1 + 6*x2 >= 8)
    model.addConstr(49*x0**2 + 9*x1**2 >= 20)
    model.addConstr(7*x0 + 3*x1 + 6*x2 >= 20)
    model.addConstr(2*x1 + 6*x2 >= 18)
    model.addConstr(64*x0**2 + 36*x2**2 >= 20)
    model.addConstr(8*x0 + 2*x1 + 6*x2 >= 22)
    model.addConstr(4*x1 - 5*x2 >= 0)
    model.addConstr(10*x0**2 - 5*x2**2 >= 0)
    model.addConstr(7*x0 + 8*x1 <= 74)
    model.addConstr(8*x1 + 8*x2 <= 75)
    model.addConstr(7*x0 + 6*x2 <= 57)
    model.addConstr(49*x0**2 + 9*x1**2 + 36*x2**2 <= 53)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```