## Step 1: Define the symbolic representation of the variables
The variables are 'paper towel rolls' and 'candles', which we can represent symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $6.32x_1 + 6.34x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $4x_1 + 9x_2 \geq 54$
2. $15x_1 + 17x_2 \geq 55$
3. $4x_1 - 3x_2 \geq 0$
4. $4x_1 + 9x_2 \leq 178$
5. $15x_1 + 17x_2 \leq 86$
6. $x_1 \geq 0$ and $x_1$ is an integer
7. $x_2 \geq 0$ and $x_2$ is an integer

## 4: Compile the symbolic representation into a JSON object
```json
{
'sym_variables': [('x1', 'paper towel rolls'), ('x2', 'candles')],
'objective_function': '6.32*x1 + 6.34*x2',
'constraints': [
'4*x1 + 9*x2 >= 54',
'15*x1 + 17*x2 >= 55',
'4*x1 - 3*x2 >= 0',
'4*x1 + 9*x2 <= 178',
'15*x1 + 17*x2 <= 86',
'x1 >= 0, x1 is an integer',
'x2 >= 0, x2 is an integer'
]
}
```

## Step 5: Translate the problem into Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

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

# Objective function
model.setObjective(6.32 * x1 + 6.34 * x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(4 * x1 + 9 * x2 >= 54)
model.addConstr(15 * x1 + 17 * x2 >= 55)
model.addConstr(4 * x1 - 3 * x2 >= 0)
model.addConstr(4 * x1 + 9 * x2 <= 178)
model.addConstr(15 * x1 + 17 * x2 <= 86)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Paper towel rolls: {x1.varValue}")
    print(f"Candles: {x2.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```