## Step 1: Define the symbolic representation of the variables
The variables are ['headsets', 'scissors', 'blue pens', 'blue highlighters', 'color printers'] which can be represented symbolically as ['x1', 'x2', 'x3', 'x4', 'x5'].

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is: 
\[ 7.04x_1^2 + 3.25x_1x_2 + 7.47x_1x_3 + 8.76x_1x_4 + 9.02x_1x_5 + 1.01x_2^2 + 6.49x_2x_3 + 9.89x_2x_4 + 9.84x_3^2 + 9.76x_3x_5 + 6.46x_4x_5 + 7.63x_2 + 4.82x_3 + 4.36x_5 \]

## 3: Define the constraints in symbolic notation
The constraints are:
- $3x_1 + 7x_4 \geq 40$
- $4^2x_2^2 + 7^2x_3^2 \geq 22$
- $7x_3 + 5x_5 \geq 28$
- $4x_2 + 7x_4 \geq 46$
- $3x_1 + 5x_5 \geq 21$
- $7^2x_3^2 + 7^2x_4^2 \geq 47$
- $3x_1 + 4x_2 + 7x_4 \geq 44$
- $4x_2 + 7x_3 \leq 194$
- $3^2x_1^2 + 7^2x_3^2 \leq 51$
- $7^2x_3^2 + 5^2x_5^2 \leq 157$
- $4x_2 + 5x_5 \leq 91$
- $4x_2 + 7x_4 + 5x_5 \leq 101$
- $3^2x_1^2 + 4^2x_2^2 + 5^2x_5^2 \leq 162$
- $3x_1 + 7x_3 + 5x_5 \leq 234$
- $7x_3 + 7x_4 + 5x_5 \leq 240$
- $3x_1 + 4x_2 + 7x_3 + 7x_4 + 5x_5 \leq 240$

## 4: Express the problem in a JSON format for clarity
```json
{
    'sym_variables': [
        ('x1', 'headsets'), 
        ('x2', 'scissors'), 
        ('x3', 'blue pens'), 
        ('x4', 'blue highlighters'), 
        ('x5', 'color printers')
    ],
    'objective_function': '7.04*x1^2 + 3.25*x1*x2 + 7.47*x1*x3 + 8.76*x1*x4 + 9.02*x1*x5 + 1.01*x2^2 + 6.49*x2*x3 + 9.89*x2*x4 + 9.84*x3^2 + 9.76*x3*x5 + 6.46*x4*x5 + 7.63*x2 + 4.82*x3 + 4.36*x5',
    'constraints': [
        '3*x1 + 7*x4 >= 40',
        '16*x2^2 + 49*x3^2 >= 22',
        '7*x3 + 5*x5 >= 28',
        '4*x2 + 7*x4 >= 46',
        '3*x1 + 5*x5 >= 21',
        '49*x3^2 + 49*x4^2 >= 47',
        '3*x1 + 4*x2 + 7*x4 >= 44',
        '4*x2 + 7*x3 <= 194',
        '9*x1^2 + 49*x3^2 <= 51',
        '49*x3^2 + 25*x5^2 <= 157',
        '4*x2 + 5*x5 <= 91',
        '4*x2 + 7*x4 + 5*x5 <= 101',
        '9*x1^2 + 16*x2^2 + 25*x5^2 <= 162',
        '3*x1 + 7*x3 + 5*x5 <= 234',
        '7*x3 + 7*x4 + 5*x5 <= 240',
        '3*x1 + 4*x2 + 7*x3 + 7*x4 + 5*x5 <= 240'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="headsets", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="scissors", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="blue pens", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="blue highlighters", vtype=gurobi.GRB.INTEGER)
    x5 = model.addVar(name="color printers", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(7.04*x1**2 + 3.25*x1*x2 + 7.47*x1*x3 + 8.76*x1*x4 + 9.02*x1*x5 + 
                      1.01*x2**2 + 6.49*x2*x3 + 9.89*x2*x4 + 9.84*x3**2 + 9.76*x3*x5 + 
                      6.46*x4*x5 + 7.63*x2 + 4.82*x3 + 4.36*x5, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3*x1 + 7*x4 >= 40)
    model.addConstr(16*x2**2 + 49*x3**2 >= 22)
    model.addConstr(7*x3 + 5*x5 >= 28)
    model.addConstr(4*x2 + 7*x4 >= 46)
    model.addConstr(3*x1 + 5*x5 >= 21)
    model.addConstr(49*x3**2 + 49*x4**2 >= 47)
    model.addConstr(3*x1 + 4*x2 + 7*x4 >= 44)
    model.addConstr(4*x2 + 7*x3 <= 194)
    model.addConstr(9*x1**2 + 49*x3**2 <= 51)
    model.addConstr(49*x3**2 + 25*x5**2 <= 157)
    model.addConstr(4*x2 + 5*x5 <= 91)
    model.addConstr(4*x2 + 7*x4 + 5*x5 <= 101)
    model.addConstr(9*x1**2 + 16*x2**2 + 25*x5**2 <= 162)
    model.addConstr(3*x1 + 7*x3 + 5*x5 <= 234)
    model.addConstr(7*x3 + 7*x4 + 5*x5 <= 240)
    model.addConstr(3*x1 + 4*x2 + 7*x3 + 7*x4 + 5*x5 <= 240)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Headsets: ", x1.varValue)
        print("Scissors: ", x2.varValue)
        print("Blue Pens: ", x3.varValue)
        print("Blue Highlighters: ", x4.varValue)
        print("Color Printers: ", x5.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```