## Step 1: Define the symbolic representation of the variables
The variables are 'rubber bands', 'monochrome printers', and 'red pens', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $9.37x_0^2 + 3.14x_1x_2 + 8.57x_0 + 1.97x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $12x_0 + 6x_1 + 4x_2 \geq 76$
- $27^2x_0^2 + 17^2x_1^2 + 16^2x_2^2 \geq 54$
- $12x_0 + 6x_1 \leq 212$
- $12^2x_0^2 + 4^2x_2^2 \leq 296$
- $12x_0 + 6x_1 + 4x_2 \leq 296$
- $17^2x_1^2 + 16^2x_2^2 \leq 90$
- $27^2x_0^2 + 17^2x_1^2 \leq 193$
- $27x_0 + 17x_1 + 16x_2 \leq 193$
- $x_0, x_1, x_2$ are integers.

## 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'rubber bands'), ('x1', 'monochrome printers'), ('x2', 'red pens')],
'objective_function': '9.37*x0^2 + 3.14*x1*x2 + 8.57*x0 + 1.97*x2',
'constraints': [
    '12*x0 + 6*x1 + 4*x2 >= 76',
    '729*x0^2 + 289*x1^2 + 256*x2^2 >= 54',
    '12*x0 + 6*x1 <= 212',
    '144*x0^2 + 16*x2^2 <= 296',
    '12*x0 + 6*x1 + 4*x2 <= 296',
    '289*x1^2 + 256*x2^2 <= 90',
    '729*x0^2 + 289*x1^2 <= 193',
    '27*x0 + 17*x1 + 16*x2 <= 193',
    'x0, x1, x2 are integers'
]
}
```

## Step 5: Write the Gurobi code for the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="rubber_bands", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="monochrome_printers", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="red_pens", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(9.37 * x0**2 + 3.14 * x1 * x2 + 8.57 * x0 + 1.97 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(12 * x0 + 6 * x1 + 4 * x2 >= 76)
    model.addConstr(729 * x0**2 + 289 * x1**2 + 256 * x2**2 >= 54)
    model.addConstr(12 * x0 + 6 * x1 <= 212)
    model.addConstr(144 * x0**2 + 16 * x2**2 <= 296)
    model.addConstr(12 * x0 + 6 * x1 + 4 * x2 <= 296)
    model.addConstr(289 * x1**2 + 256 * x2**2 <= 90)
    model.addConstr(729 * x0**2 + 289 * x1**2 <= 193)
    model.addConstr(27 * x0 + 17 * x1 + 16 * x2 <= 193)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Rubber bands: {x0.varValue}")
        print(f"Monochrome printers: {x1.varValue}")
        print(f"Red pens: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```