To tackle this problem, we first need to translate the given natural language description into a symbolic representation that can be used to formulate an optimization model. The variables and constraints provided in the problem statement will guide us in creating this representation.

Given variables:
- `x0` represents '3D printers'
- `x1` represents 'packs of paper'

Objective Function:
The objective is to minimize the value of `6 * x0 * x1 + 8 * x1`.

Constraints:
1. Dollar cost constraint: `6 * x0 + 9 * x1 <= 100`
2. Weight constraint: `20 * x0 + 9 * x1 <= 178`
3. Minimum dollar spend on 3D printers and packs of paper: `6 * x0 + 9 * x1 >= 33`
4. Combined weight must be at least 84 pounds: `20 * x0 + 9 * x1 >= 84`
5. Constraint involving number of 3D printers and packs of paper: `x0 - 4 * x1 >= 0`
6. Maximum dollar spend on 3D printers plus packs of paper: `6 * x0 + 9 * x1 <= 70`
7. Combined weight should not exceed 168 pounds: `20 * x0 + 9 * x1 <= 168`
8. Integer constraint for the number of 3D printers: `x0` must be an integer
9. Integer constraint for packs of paper: `x1` must be an integer

Symbolic Representation:
```json
{
    'sym_variables': [('x0', '3D printers'), ('x1', 'packs of paper')],
    'objective_function': '6 * x0 * x1 + 8 * x1',
    'constraints': [
        '6 * x0 + 9 * x1 <= 100',
        '20 * x0 + 9 * x1 <= 178',
        '6 * x0 + 9 * x1 >= 33',
        '20 * x0 + 9 * x1 >= 84',
        'x0 - 4 * x1 >= 0',
        '6 * x0 + 9 * x1 <= 70',
        '20 * x0 + 9 * x1 <= 168',
        'x0 == int(x0)',
        'x1 == int(x1)'
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="3D_printers")
x1 = m.addVar(vtype=GRB.INTEGER, name="packs_of_paper")

# Set objective function
m.setObjective(6 * x0 * x1 + 8 * x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(6 * x0 + 9 * x1 <= 100, "dollar_cost")
m.addConstr(20 * x0 + 9 * x1 <= 178, "weight")
m.addConstr(6 * x0 + 9 * x1 >= 33, "min_dollar_spend")
m.addConstr(20 * x0 + 9 * x1 >= 84, "min_weight")
m.addConstr(x0 - 4 * x1 >= 0, "printer_paper_ratio")
m.addConstr(6 * x0 + 9 * x1 <= 70, "max_dollar_spend")
m.addConstr(20 * x0 + 9 * x1 <= 168, "max_weight")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"3D printers: {x0.x}")
    print(f"Packs of paper: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```