## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'packs of paper plates' and 'candles', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $1 \cdot x_1 + 5 \cdot x_2$. The constraints are:
- $5x_1 + 8x_2 \geq 35$
- $x_1 + 2x_2 \geq 7$
- $-4x_1 + 9x_2 \geq 0$
- $5x_1 + 8x_2 \leq 54$
- $x_1 + 2x_2 \leq 39$
- $x_1$ is a non-negative integer
- $x_2$ is a non-negative integer

## Step 2: Convert the problem into a symbolic representation
The symbolic representation is as follows:
```json
{
'sym_variables': [('x1', 'packs of paper plates'), ('x2', 'candles')],
'objective_function': '1*x1 + 5*x2',
'constraints': [
    '5*x1 + 8*x2 >= 35',
    'x1 + 2*x2 >= 7',
    '-4*x1 + 9*x2 >= 0',
    '5*x1 + 8*x2 <= 54',
    'x1 + 2*x2 <= 39',
    'x1 >= 0 and x1 is an integer',
    'x2 >= 0 and x2 is an integer'
]
}
```

## 3: Implement the problem using Gurobi
To solve this problem using Gurobi, we will use the Gurobi Python API. We need to import the Gurobi library, create a model, add variables and constraints, and then solve the model.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="packs_of_paper_plates", vtype=gp.GRB.INTEGER)  # packs of paper plates
x2 = m.addVar(name="candles", vtype=gp.GRB.INTEGER)  # candles

# Objective function: minimize 1*x1 + 5*x2
m.setObjective(x1 + 5*x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(5*x1 + 8*x2 >= 35, name="total_value_min")
m.addConstr(x1 + 2*x2 >= 7, name="total_portability_min")
m.addConstr(-4*x1 + 9*x2 >= 0, name="combined_value_constraint")
m.addConstr(5*x1 + 8*x2 <= 54, name="total_value_max")
m.addConstr(x1 + 2*x2 <= 39, name="total_portability_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("packs of paper plates: ", x1.varValue)
    print("candles: ", x2.varValue)
else:
    print("The model is infeasible")
```