## Step 1: Define the symbolic representation of the variables
The variables are '3D printers' and 'packs of paper', 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 $6x_1x_2 + 8x_2$.

## Step 3: List all the constraints in symbolic notation
1. $6x_1 + 9x_2 \geq 33$ (spend at least $33)
2. $20x_1 + 9x_2 \geq 84$ (combined weight of at least 84 pounds)
3. $x_1 - 4x_2 \geq 0$ (relationship between 3D printers and packs of paper)
4. $6x_1 + 9x_2 \leq 70$ (spend no more than $70)
5. $20x_1 + 9x_2 \leq 168$ (combined weight of no more than 168 pounds)
6. $x_1 \in \mathbb{Z}$ (integer number of 3D printers)
7. $x_2 \in \mathbb{Z}$ (integer number of packs of paper)

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', '3D printers'), ('x2', 'packs of paper')],
    'objective_function': '6*x1*x2 + 8*x2',
    'constraints': [
        '6*x1 + 9*x2 >= 33',
        '20*x1 + 9*x2 >= 84',
        'x1 - 4*x2 >= 0',
        '6*x1 + 9*x2 <= 70',
        '20*x1 + 9*x2 <= 168',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="3D_printers", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="packs_of_paper", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(6 * x1 * x2 + 8 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(6 * x1 + 9 * x2 >= 33)
    model.addConstr(20 * x1 + 9 * x2 >= 84)
    model.addConstr(x1 - 4 * x2 >= 0)
    model.addConstr(6 * x1 + 9 * x2 <= 70)
    model.addConstr(20 * x1 + 9 * x2 <= 168)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"3D printers: {x1.varValue}")
        print(f"Packs of paper: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```