## Step 1: Define the symbolic representation of the variables
The variables are 'cafeteria chairs', 'blue pens', and 'color printers', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : cafeteria chairs
- $x_1$ : blue pens
- $x_2$ : color printers

## 3: Define the objective function in symbolic notation
The objective function to maximize is $4.64x_0 + 3.66x_1 + 7.16x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $8x_0 + 13x_1 + 9x_2 \geq 22$
- $15x_1 + 2x_2 \geq 22$
- $10x_0 + 15x_1 \geq 35$
- $10x_0 + 2x_2 \geq 42$
- $13x_1 + 9x_2 \leq 52$
- $8x_0 + 13x_1 + 9x_2 \leq 52$
- $10x_0 + 15x_1 \leq 164$
- $10x_0 + 15x_1 + 2x_2 \leq 164$
- $x_0 \in \mathbb{Z}$
- $x_1 \in \mathbb{Z}$
- $x_2 \in \mathbb{Z}$

## 5: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x0', 'cafeteria chairs'), ('x1', 'blue pens'), ('x2', 'color printers')],
    'objective_function': '4.64*x0 + 3.66*x1 + 7.16*x2',
    'constraints': [
        '8*x0 + 13*x1 + 9*x2 >= 22',
        '15*x1 + 2*x2 >= 22',
        '10*x0 + 15*x1 >= 35',
        '10*x0 + 2*x2 >= 42',
        '13*x1 + 9*x2 <= 52',
        '8*x0 + 13*x1 + 9*x2 <= 52',
        '10*x0 + 15*x1 <= 164',
        '10*x0 + 15*x1 + 2*x2 <= 164',
        'x0 >= 0 and x0 in Integer',
        'x1 >= 0 and x1 in Integer',
        'x2 >= 0 and x2 in Integer'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name='cafeteria_chairs', vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name='blue_pens', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='color_printers', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(4.64 * x0 + 3.66 * x1 + 7.16 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(8 * x0 + 13 * x1 + 9 * x2 >= 22)
    model.addConstr(15 * x1 + 2 * x2 >= 22)
    model.addConstr(10 * x0 + 15 * x1 >= 35)
    model.addConstr(10 * x0 + 2 * x2 >= 42)
    model.addConstr(13 * x1 + 9 * x2 <= 52)
    model.addConstr(8 * x0 + 13 * x1 + 9 * x2 <= 52)
    model.addConstr(10 * x0 + 15 * x1 <= 164)
    model.addConstr(10 * x0 + 15 * x1 + 2 * x2 <= 164)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Cafeteria Chairs: ', x0.varValue)
        print('Blue Pens: ', x1.varValue)
        print('Color Printers: ', x2.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```