## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'cans of coffee' and 'paper clips', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $4.13x_1 + 4.5x_2$. The constraints are:
- $10x_1 + 8x_2 \geq 32$
- $7x_1 + 17x_2 \geq 34$
- $13x_1 + 11x_2 \geq 25$
- $8x_1 - 3x_2 \geq 0$
- $10x_1 + 8x_2 \leq 82$
- $7x_1 + 17x_2 \leq 94$
- $13x_1 + 11x_2 \leq 25$
- $x_1$ and $x_2$ are integers.

## Step 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for 'cans of coffee'
- $x_2$ for 'paper clips'

The objective function is: $4.13x_1 + 4.5x_2$

The constraints are:
- $10x_1 + 8x_2 \geq 32$
- $7x_1 + 17x_2 \geq 34$
- $13x_1 + 11x_2 \geq 25$
- $8x_1 - 3x_2 \geq 0$
- $10x_1 + 8x_2 \leq 82$
- $7x_1 + 17x_2 \leq 94$
- $13x_1 + 11x_2 \leq 25$

## 3: Write down the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'cans of coffee'), ('x2', 'paper clips')],
    'objective_function': '4.13*x1 + 4.5*x2',
    'constraints': [
        '10*x1 + 8*x2 >= 32',
        '7*x1 + 17*x2 >= 34',
        '13*x1 + 11*x2 >= 25',
        '8*x1 - 3*x2 >= 0',
        '10*x1 + 8*x2 <= 82',
        '7*x1 + 17*x2 <= 94',
        '13*x1 + 11*x2 <= 25',
        'x1 >= 0 and x1 is an integer',
        'x2 >= 0 and x2 is an integer'
    ]
}
```

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

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

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

    # Define the objective function
    model.setObjective(4.13 * x1 + 4.5 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(10 * x1 + 8 * x2 >= 32)
    model.addConstr(7 * x1 + 17 * x2 >= 34)
    model.addConstr(13 * x1 + 11 * x2 >= 25)
    model.addConstr(8 * x1 - 3 * x2 >= 0)
    model.addConstr(10 * x1 + 8 * x2 <= 82)
    model.addConstr(7 * x1 + 17 * x2 <= 94)
    model.addConstr(13 * x1 + 11 * x2 <= 25)
    model.addConstr(x1 >= 0)
    model.addConstr(x2 >= 0)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```