To solve this optimization problem, we first need to define the variables and the objective function symbolically, followed by translating the constraints into a suitable format. Then, we'll use Gurobi to find the optimal solution.

### Symbolic Representation

Let's denote:
- $x_1$ as the number of 'black pens',
- $x_2$ as the number of 'cafeteria chairs',
- $x_3$ as the number of 'staplers'.

The objective function to minimize is: $8x_1 + 9x_2 + 5x_3$.

Constraints:
1. Usefulness rating from black pens and cafeteria chairs: $16x_1 + 18x_2 \geq 29$
2. Total usefulness rating including staplers: $16x_1 + 18x_2 + 11x_3 \geq 29$
3. Constraint involving black pens and staplers: $-10x_1 + 4x_3 \geq 0$
4. Constraint involving cafeteria chairs and staplers: $-x_2 + 5x_3 \geq 0$
5. Constraint involving black pens and cafeteria chairs: $10x_1 - 4x_2 \geq 0$
6. Usefulness rating from black pens and staplers: $16x_1 + 11x_3 \leq 82$
7. Usefulness rating from cafeteria chairs and staplers: $18x_2 + 11x_3 \leq 72$

All variables are integers.

### JSON Representation
```json
{
    'sym_variables': [('x1', 'black pens'), ('x2', 'cafeteria chairs'), ('x3', 'staplers')],
    'objective_function': '8*x1 + 9*x2 + 5*x3',
    'constraints': [
        '16*x1 + 18*x2 >= 29',
        '16*x1 + 18*x2 + 11*x3 >= 29',
        '-10*x1 + 4*x3 >= 0',
        '-x2 + 5*x3 >= 0',
        '10*x1 - 4*x2 >= 0',
        '16*x1 + 11*x3 <= 82',
        '18*x2 + 11*x3 <= 72'
    ]
}
```

### Gurobi Code
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(vtype=GRB.INTEGER, name="black_pens")
x2 = m.addVar(vtype=GRB.INTEGER, name="cafeteria_chairs")
x3 = m.addVar(vtype=GRB.INTEGER, name="staplers")

# Set the objective function
m.setObjective(8*x1 + 9*x2 + 5*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(16*x1 + 18*x2 >= 29, "usefulness_rating_bc")
m.addConstr(16*x1 + 18*x2 + 11*x3 >= 29, "total_usefulness_rating")
m.addConstr(-10*x1 + 4*x3 >= 0, "black_pens_staplers")
m.addConstr(-x2 + 5*x3 >= 0, "cafeteria_chairs_staplers")
m.addConstr(10*x1 - 4*x2 >= 0, "black_pens_cafeteria_chairs")
m.addConstr(16*x1 + 11*x3 <= 82, "usefulness_rating_bs")
m.addConstr(18*x2 + 11*x3 <= 72, "usefulness_rating_cs")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Black Pens: {x1.x}")
    print(f"Cafeteria Chairs: {x2.x}")
    print(f"Staplers: {x3.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```