## Step 1: Define the optimization problem
The problem is to maximize the objective function: $2 \times \text{headsets} + 3 \times \text{rubber bands} + 5 \times \text{planners} + 7 \times \text{hole punches}$, subject to various constraints on storage space and weight.

## Step 2: List all the constraints
1. $0.5 \times \text{headsets} + 2.54 \times \text{rubber bands} + 0.12 \times \text{planners} + 2.75 \times \text{hole punches} \leq 222$ (storage space)
2. $1.49 \times \text{headsets} + 0.16 \times \text{rubber bands} + 0.33 \times \text{planners} + 2.73 \times \text{hole punches} \leq 231$ (weight)
3. $0.5 \times \text{headsets} + 0.12 \times \text{planners} + 2.75 \times \text{hole punches} \geq 45$ (storage space usage)
4. $0.5 \times \text{headsets} + 2.54 \times \text{rubber bands} + 0.12 \times \text{planners} \geq 45$ (storage space usage)
5. $0.5 \times \text{headsets} + 0.12 \times \text{planners} + 2.75 \times \text{hole punches} \geq 36$ (storage space usage)
6. $0.5 \times \text{headsets} + 2.54 \times \text{rubber bands} + 0.12 \times \text{planners} \geq 36$ (storage space usage)
7. $1.49 \times \text{headsets} + 0.16 \times \text{rubber bands} \geq 39$ (weight)
8. $0.16 \times \text{rubber bands} + 0.33 \times \text{planners} \geq 54$ (weight)
9. $0.5 \times \text{headsets} + 2.54 \times \text{rubber bands} \leq 164$ (storage space)
10. $2.54 \times \text{rubber bands} + 0.12 \times \text{planners} \leq 104$ (storage space)
11. $0.5 \times \text{headsets} + 0.12 \times \text{planners} \leq 101$ (storage space)
12. $2.54 \times \text{rubber bands} + 2.75 \times \text{hole punches} \leq 92$ (storage space)
13. $0.5 \times \text{headsets} + 2.54 \times \text{rubber bands} + 0.12 \times \text{planners} + 2.75 \times \text{hole punches} \leq 92$ (storage space)
14. $0.16 \times \text{rubber bands} + 0.33 \times \text{planners} \leq 177$ (weight)
15. $1.49 \times \text{headsets} + 0.33 \times \text{planners} \leq 190$ (weight)
16. $0.33 \times \text{planners} + 2.73 \times \text{hole punches} \leq 85$ (weight)
17. $1.49 \times \text{headsets} + 0.16 \times \text{rubber bands} + 0.33 \times \text{planners} + 2.73 \times \text{hole punches} \leq 85$ (weight)

## Step 3: Define the variables and objective function in Gurobi
We will use Gurobi to solve this linear programming problem. The variables are defined as follows:
- `headsets`
- `rubber bands`
- `planners`
- `hole punches`

## 4: Implement the problem in Gurobi
```python
import gurobi

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

    # Define the variables
    headsets = model.addVar(name="headsets", vtype=gurobi.GRB.INTEGER)
    rubber_bands = model.addVar(name="rubber_bands", vtype=gurobi.GRB.INTEGER)
    planners = model.addVar(name="planners", vtype=gurobi.GRB.INTEGER)
    hole_punches = model.addVar(name="hole_punches", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(2 * headsets + 3 * rubber_bands + 5 * planners + 7 * hole_punches, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.5 * headsets + 2.54 * rubber_bands + 0.12 * planners + 2.75 * hole_punches <= 222)
    model.addConstr(1.49 * headsets + 0.16 * rubber_bands + 0.33 * planners + 2.73 * hole_punches <= 231)
    model.addConstr(0.5 * headsets + 0.12 * planners + 2.75 * hole_punches >= 45)
    model.addConstr(0.5 * headsets + 2.54 * rubber_bands + 0.12 * planners >= 45)
    model.addConstr(0.5 * headsets + 0.12 * planners + 2.75 * hole_punches >= 36)
    model.addConstr(0.5 * headsets + 2.54 * rubber_bands + 0.12 * planners >= 36)
    model.addConstr(1.49 * headsets + 0.16 * rubber_bands >= 39)
    model.addConstr(0.16 * rubber_bands + 0.33 * planners >= 54)
    model.addConstr(0.5 * headsets + 2.54 * rubber_bands <= 164)
    model.addConstr(2.54 * rubber_bands + 0.12 * planners <= 104)
    model.addConstr(0.5 * headsets + 0.12 * planners <= 101)
    model.addConstr(2.54 * rubber_bands + 2.75 * hole_punches <= 92)
    model.addConstr(0.5 * headsets + 2.54 * rubber_bands + 0.12 * planners + 2.75 * hole_punches <= 92)
    model.addConstr(0.16 * rubber_bands + 0.33 * planners <= 177)
    model.addConstr(1.49 * headsets + 0.33 * planners <= 190)
    model.addConstr(0.33 * planners + 2.73 * hole_punches <= 85)
    model.addConstr(1.49 * headsets + 0.16 * rubber_bands + 0.33 * planners + 2.73 * hole_punches <= 85)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Headsets: {headsets.varValue}")
        print(f"Rubber Bands: {rubber_bands.varValue}")
        print(f"Planners: {planners.varValue}")
        print(f"Hole Punches: {hole_punches.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```