## Step 1: Define the symbolic representation of the variables
The variables are 'manila envelopes' and 'hole punches', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $6.04x_1 + 3.72x_2$.

## Step 3: List all the constraints in symbolic notation
1. $12x_1 + 14x_2 \geq 26$ (Total cost at least $26)
2. $12x_1 + 14x_2 \geq 26$ (Same as the first constraint, ensuring at least $26 spend)
3. $x_1 + 14x_2 \geq 9$ (Storage space at least 9 sq. ft)
4. $8x_1 + 8x_2 \geq 39$ (Workplace safety impact at least 39)
5. $6x_1 + 4x_2 \geq 38$ (Employee satisfaction impact at least 38)
6. $5x_1 - 3x_2 \geq 0$ (Specific relationship between manila envelopes and hole punches)
7. $12x_1 + 14x_2 \leq 55$ (Total spend at most $55)
8. $x_1 + 14x_2 \leq 42$ (Storage space at most 42 sq. ft)
9. $8x_1 + 8x_2 \leq 43$ (Workplace safety impact at most 43)
10. $6x_1 + 4x_2 \leq 83$ (Employee satisfaction impact at most 83)
11. $x_1 \in \mathbb{Z}$ (Integer number of manila envelopes)
12. $x_2 \in \mathbb{Z}$ (Integer number of hole punches)

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'manila envelopes'), ('x2', 'hole punches')],
    'objective_function': '6.04*x1 + 3.72*x2',
    'constraints': [
        '12*x1 + 14*x2 >= 26',
        'x1 + 14*x2 >= 9',
        '8*x1 + 8*x2 >= 39',
        '6*x1 + 4*x2 >= 38',
        '5*x1 - 3*x2 >= 0',
        '12*x1 + 14*x2 <= 55',
        'x1 + 14*x2 <= 42',
        '8*x1 + 8*x2 <= 43',
        '6*x1 + 4*x2 <= 83'
    ],
    'integrality_constraints': ['x1', 'x2']
}
```

## 5: 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
    x1 = model.addVar(name='manila_envelopes', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hole_punches', vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6.04 * x1 + 3.72 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(12 * x1 + 14 * x2 >= 26)
    model.addConstr(x1 + 14 * x2 >= 9)
    model.addConstr(8 * x1 + 8 * x2 >= 39)
    model.addConstr(6 * x1 + 4 * x2 >= 38)
    model.addConstr(5 * x1 - 3 * x2 >= 0)
    model.addConstr(12 * x1 + 14 * x2 <= 55)
    model.addConstr(x1 + 14 * x2 <= 42)
    model.addConstr(8 * x1 + 8 * x2 <= 43)
    model.addConstr(6 * x1 + 4 * x2 <= 83)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Manila envelopes: ', x1.varValue)
        print('Hole punches: ', x2.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```