## Step 1: Define the symbolic representation of the variables
The variables are 'mechanical pencils' and 'headsets', which can be represented symbolically as $x_0$ and $x_1$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $1.36x_0 + 8.25x_1$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $9x_0 + 8x_1 \geq 44$
- $9x_0 + 8x_1 \geq 44$ (same as the previous one, so we keep only one)
- $5x_0 + 8x_1 \geq 11$
- $5x_0 + 8x_1 \geq 11$ (same as the previous one, so we keep only one)
- $2x_0 + 2x_1 \geq 39$
- $2x_0 + 2x_1 \geq 39$ (same as the previous one, so we keep only one)
- $3x_0 - 3x_1 \geq 0$
- $9x_0 + 8x_1 \leq 48$
- $5x_0 + 8x_1 \leq 25$
- $2x_0 + 2x_1 \leq 71$
- $x_0$ and $x_1$ are integers.

## 4: Convert the problem into a Gurobi model
We will use Gurobi to solve this optimization problem.

## 5: Write the Gurobi code
```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="mechanical_pencils", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="headsets", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(1.36 * x0 + 8.25 * x1, gp.GRB.MINIMIZE)

# Define the constraints
m.addConstr(9 * x0 + 8 * x1 >= 44, name="employee_satisfaction_impact")
m.addConstr(5 * x0 + 8 * x1 >= 11, name="usefulness_rating")
m.addConstr(2 * x0 + 2 * x1 >= 39, name="storage_space")
m.addConstr(3 * x0 - 3 * x1 >= 0, name="balance_constraint")
m.addConstr(9 * x0 + 8 * x1 <= 48, name="max_employee_satisfaction_impact")
m.addConstr(5 * x0 + 8 * x1 <= 25, name="max_usefulness_rating")
m.addConstr(2 * x0 + 2 * x1 <= 71, name="max_storage_space")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Mechanical Pencils: ", x0.varValue)
    print("Headsets: ", x1.varValue)
else:
    print("The model is infeasible")
```

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'mechanical pencils'), ('x1', 'headsets')],
    'objective_function': '1.36*x0 + 8.25*x1',
    'constraints': [
        '9*x0 + 8*x1 >= 44',
        '5*x0 + 8*x1 >= 11',
        '2*x0 + 2*x1 >= 39',
        '3*x0 - 3*x1 >= 0',
        '9*x0 + 8*x1 <= 48',
        '5*x0 + 8*x1 <= 25',
        '2*x0 + 2*x1 <= 71'
    ]
}
```