## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'cafeteria chairs' and 'office chairs', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $5.69x_1 + 1.68x_2$. The constraints are:
- $18.72x_1 + 22.68x_2 \geq 40$
- $18.72x_1 + 22.68x_2 \leq 142$
- $4.65x_1 + 0.75x_2 \geq 131$
- $4.65x_1 + 0.75x_2 \leq 236$
- $3.38x_1 + 13.07x_2 \geq 31$
- $3.38x_1 + 13.07x_2 \leq 59$
- $12.35x_1 + 3.1x_2 \geq 44$
- $12.35x_1 + 3.1x_2 \leq 198$
- $25.61x_1 + 20.04x_2 \geq 97$
- $25.61x_1 + 20.04x_2 \leq 228$
- $-8x_1 + 9x_2 \geq 0$
- $x_1, x_2$ are integers.

## Step 2: Convert the problem into a Gurobi-compatible format
We need to define the variables, the objective function, and the constraints in a way that Gurobi can understand.

## 3: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="cafeteria_chairs", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="office_chairs", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(5.69 * x1 + 1.68 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(18.72 * x1 + 22.68 * x2 >= 40, name="workplace_safety_impact")
    model.addConstr(4.65 * x1 + 0.75 * x2 >= 131, name="weight")
    model.addConstr(3.38 * x1 + 13.07 * x2 >= 31, name="usefulness_rating")
    model.addConstr(12.35 * x1 + 3.1 * x2 >= 44, name="storage_space")
    model.addConstr(25.61 * x1 + 20.04 * x2 >= 97, name="dollar_cost")
    model.addConstr(-8 * x1 + 9 * x2 >= 0, name="linear_constraint")

    model.addConstr(18.72 * x1 + 22.68 * x2 <= 142, name="workplace_safety_impact_upper")
    model.addConstr(4.65 * x1 + 0.75 * x2 <= 236, name="weight_upper")
    model.addConstr(3.38 * x1 + 13.07 * x2 <= 59, name="usefulness_rating_upper")
    model.addConstr(12.35 * x1 + 3.1 * x2 <= 198, name="storage_space_upper")
    model.addConstr(25.61 * x1 + 20.04 * x2 <= 228, name="dollar_cost_upper")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Cafeteria chairs: {x1.varValue}")
        print(f"Office chairs: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```

## Step 4: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'cafeteria chairs'), ('x2', 'office chairs')],
    'objective_function': '5.69*x1 + 1.68*x2',
    'constraints': [
        '18.72*x1 + 22.68*x2 >= 40',
        '18.72*x1 + 22.68*x2 <= 142',
        '4.65*x1 + 0.75*x2 >= 131',
        '4.65*x1 + 0.75*x2 <= 236',
        '3.38*x1 + 13.07*x2 >= 31',
        '3.38*x1 + 13.07*x2 <= 59',
        '12.35*x1 + 3.1*x2 >= 44',
        '12.35*x1 + 3.1*x2 <= 198',
        '25.61*x1 + 20.04*x2 >= 97',
        '25.61*x1 + 20.04*x2 <= 228',
        '-8*x1 + 9*x2 >= 0'
    ]
}
```