## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ represents 'packs of napkins'
- $x_2$ represents 'dish soap bottles'
- $x_3$ represents 'paper towel rolls'
- $x_4$ represents 'toilet paper rolls'

## Step 2: Formulate the objective function
The objective function to minimize is $10.0x_1 + 6.84x_2 + 5.05x_3 + 1.44x_4$.

## Step 3: Define the constraints
The constraints are:
1. $8x_1 + 4x_2 + 3x_3 + 6x_4 \leq 97$ (storage space constraint)
2. $8x_1 \geq 24$ (packs of napkins and storage space)
3. $x_1 + x_3 \geq 3$ (packs of napkins and paper towel rolls storage space, adjusted for correct units)
4. $4x_2 + 3x_3 \geq 18$ (dish soap bottles and paper towel rolls storage space)
5. $8x_1 + 6x_4 \geq 11$ (packs of napkins and toilet paper rolls storage space, adjusted)
6. $8x_1 + 4x_2 + 3x_3 + 6x_4 \geq 11$ (total storage space)
7. $-7x_1 + 8x_3 \geq 0$ (relationship between packs of napkins and paper towel rolls)
8. $8x_1 + 4x_2 \leq 62$ (packs of napkins and dish soap bottles storage space)
9. $8x_1 + 4x_2 + 3x_3 \leq 73$ (packs of napkins, dish soap bottles, and paper towel rolls storage space)
10. $8x_1 + 4x_2 + 6x_4 \leq 96$ (packs of napkins, dish soap bottles, and toilet paper rolls storage space)
11. $4x_2 + 3x_3 + 6x_4 \leq 59$ (dish soap bottles, paper towel rolls, and toilet paper rolls storage space)
12. $3x_3 + 6x_4 \geq 14$ (paper towel rolls and toilet paper rolls storage space)

## 4: Correct and Adjust Constraints for Accuracy
Correcting and adjusting for accuracy and clarity:
- The constraint $x_1 + x_3 \geq 3$ seems to misunderstand the original problem; correctly it should relate to storage space, so $8x_1 + 3x_3 \geq 24$.
- Other constraints need to ensure they accurately reflect the problem statement.

## 5: Symbolic Representation
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'packs of napkins'), ('x2', 'dish soap bottles'), ('x3', 'paper towel rolls'), ('x4', 'toilet paper rolls')],
    'objective_function': '10.0*x1 + 6.84*x2 + 5.05*x3 + 1.44*x4',
    'constraints': [
        '8*x1 + 4*x2 + 3*x3 + 6*x4 <= 97',
        '8*x1 >= 24',
        '8*x1 + 3*x3 >= 24',
        '4*x2 + 3*x3 >= 18',
        '8*x1 + 6*x4 >= 11',
        '8*x1 + 4*x2 + 3*x3 + 6*x4 >= 11',
        '-7*x1 + 8*x3 >= 0',
        '8*x1 + 4*x2 <= 62',
        '8*x1 + 4*x2 + 3*x3 <= 73',
        '8*x1 + 4*x2 + 6*x4 <= 96',
        '4*x2 + 3*x3 + 6*x4 <= 59',
        '3*x3 + 6*x4 >= 14'
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name='packs_of_napkins', vtype=gurobi.GRB.INTEGER, lb=0)
    x2 = model.addVar(name='dish_soap_bottles', vtype=gurobi.GRB.INTEGER, lb=0)
    x3 = model.addVar(name='paper_towel_rolls', vtype=gurobi.GRB.INTEGER, lb=0)
    x4 = model.addVar(name='toilet_paper_rolls', vtype=gurobi.GRB.INTEGER, lb=0)

    # Objective function
    model.setObjective(10.0*x1 + 6.84*x2 + 5.05*x3 + 1.44*x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8*x1 + 4*x2 + 3*x3 + 6*x4 <= 97)
    model.addConstr(8*x1 >= 24)
    model.addConstr(8*x1 + 3*x3 >= 24)
    model.addConstr(4*x2 + 3*x3 >= 18)
    model.addConstr(8*x1 + 6*x4 >= 11)
    model.addConstr(8*x1 + 4*x2 + 3*x3 + 6*x4 >= 11)
    model.addConstr(-7*x1 + 8*x3 >= 0)
    model.addConstr(8*x1 + 4*x2 <= 62)
    model.addConstr(8*x1 + 4*x2 + 3*x3 <= 73)
    model.addConstr(8*x1 + 4*x2 + 6*x4 <= 96)
    model.addConstr(4*x2 + 3*x3 + 6*x4 <= 59)
    model.addConstr(3*x3 + 6*x4 >= 14)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('packs_of_napkins: ', x1.varValue)
        print('dish_soap_bottles: ', x2.varValue)
        print('paper_towel_rolls: ', x3.varValue)
        print('toilet_paper_rolls: ', x4.varValue)
    else:
        print('No optimal solution found')

solve_optimization_problem()
```