## Problem Description and Formulation

The problem is an optimization problem with two variables: 'packs of paper plates' and 'packs of napkins'. The goal is to maximize the objective function: 2.53 times the number of packs of paper plates plus 1.37 times the number of packs of napkins, subject to several constraints.

### Constraints

1. **Sustainability Score Constraints**:
   - Each pack of paper plates has a sustainability score of 7.
   - Each pack of napkins has a sustainability score of 9.
   - The total combined sustainability score must be at least 33.
   - The total combined sustainability score must be at most 47.

2. **Linear Constraint**:
   - 10 times the number of packs of paper plates minus 10 times the number of packs of napkins must be greater than or equal to zero.

3. **Integrality Constraints**:
   - The number of packs of paper plates must be an integer (non-fractional).
   - The number of packs of napkins must be an integer.

### Mathematical Formulation

Let \(x_0\) be the number of packs of paper plates and \(x_1\) be the number of packs of napkins.

- **Objective Function**: Maximize \(2.53x_0 + 1.37x_1\)
- **Constraints**:
  1. \(7x_0 + 9x_1 \geq 33\)
  2. \(7x_0 + 9x_1 \leq 47\)
  3. \(10x_0 - 10x_1 \geq 0\)
  4. \(x_0 \in \mathbb{Z}\) (integer)
  5. \(x_1 \in \mathbb{Z}\) (integer)

### Gurobi Code

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="packs_of_paper_plates", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="packs_of_napkins", vtype=gurobi.GRB.INTEGER)

    # Objective function: Maximize 2.53*x0 + 1.37*x1
    model.setObjective(2.53 * x0 + 1.37 * x1, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(7 * x0 + 9 * x1 >= 33, name="sustainability_score_min")
    model.addConstr(7 * x0 + 9 * x1 <= 47, name="sustainability_score_max")
    model.addConstr(10 * x0 - 10 * x1 >= 0, name="linear_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Packs of paper plates: {x0.varValue}")
        print(f"Packs of napkins: {x1.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("The model is infeasible.")

solve_optimization_problem()
```