## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The variables are '3D printers' and 'packs of paper'. The objective function to minimize is \(6 \times \text{3D printers} \times \text{packs of paper} + 8 \times \text{packs of paper}\).

The constraints are:
1. The dollar cost of 3D printers and packs of paper must be at least $33.
2. The combined weight of 3D printers and packs of paper must be at least 84 pounds.
3. \(1 \times \text{3D printers} - 4 \times \text{packs of paper} \geq 0\).
4. The total dollar cost must not exceed $70.
5. The combined weight must not exceed 168 pounds.
6. The number of 3D printers and packs of paper must be integers.

## Resource Attributes

- **3D printers**: 
  - Cost: $6
  - Weight: 20 lbs
- **packs of paper**:
  - Cost: $9
  - Weight: 9 lbs

## Gurobi Code Formulation

```python
import gurobi

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

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

    # Get variables
    x0 = model.getVarByName("3D_printers")
    x1 = model.getVarByName("packs_of_paper")

    # Objective function
    model.setObjective(6 * x0 * x1 + 8 * x1, gurobi.GRB.MINIMIZE)

    # Constraints
    # Cost constraint: 6*x0 + 9*x1 >= 33
    model.addConstr(6 * x0 + 9 * x1 >= 33, name="min_cost")

    # Weight constraint: 20*x0 + 9*x1 >= 84
    model.addConstr(20 * x0 + 9 * x1 >= 84, name="min_weight")

    # Relationship constraint: x0 - 4*x1 >= 0
    model.addConstr(x0 - 4 * x1 >= 0, name="relationship")

    # Max cost constraint: 6*x0 + 9*x1 <= 70
    model.addConstr(6 * x0 + 9 * x1 <= 70, name="max_cost")

    # Max weight constraint: 20*x0 + 9*x1 <= 168
    model.addConstr(20 * x0 + 9 * x1 <= 168, name="max_weight")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("3D Printers: ", x0.varValue)
        print("Packs of Paper: ", x1.varValue)
    else:
        print("No optimal solution found")

optimization_problem()
```