## Step 1: Define the symbolic representation of the variables
The variables are 'dish soap bottles', 'bottles of ibuprofen', and 'cookies', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $8x_0 + 4x_1 + 6x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $11x_0 + 5x_1 + 7x_2 \geq 49$ (total cost at least $49)
- $11x_0 + 5x_1 \geq 33$ (dish soap bottles and ibuprofen cost at least $33)
- $11x_0 + 7x_2 \geq 29$ (dish soap bottles and cookies cost at least $29)
- $5x_1 + 7x_2 \geq 49$ (ibuprofen and cookies cost at least $49)
- $20x_0 + 26x_1 \geq 23$ (dish soap bottles and ibuprofen value at least $23)
- $20x_0 + 18x_2 \geq 16$ (dish soap bottles and cookies value at least $16)
- $26x_1 + 18x_2 \geq 14$ (ibuprofen and cookies value at least $14)
- $20x_0 + 26x_1 + 18x_2 \geq 14$ (total value at least $14)
- $20x_0 - 4x_2 \geq 0$ (five times dish soap bottles minus four times cookies greater than or equal to zero, corrected to reflect actual given constraint: $5x_0 - 4x_2 \geq 0$)
- $4x_1 - 9x_2 \geq 0$ (four times ibuprofen minus nine times cookies greater than or equal to zero)
- $20x_0 + 18x_2 \leq 58$ (total value of dish soap bottles and cookies no greater than $58)

## 4: Specify variable bounds and types
- $x_0$ is a non-negative integer (dish soap bottles)
- $x_1$ is a non-negative integer (bottles of ibuprofen)
- $x_2$ is a non-negative integer (cookies)

## 5: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'dish soap bottles'), ('x1', 'bottles of ibuprofen'), ('x2', 'cookies')],
'objective_function': '8*x0 + 4*x1 + 6*x2',
'constraints': [
'11*x0 + 5*x1 + 7*x2 >= 49',
'11*x0 + 5*x1 >= 33',
'11*x0 + 7*x2 >= 29',
'5*x1 + 7*x2 >= 49',
'20*x0 + 26*x1 >= 23',
'20*x0 + 18*x2 >= 16',
'26*x1 + 18*x2 >= 14',
'20*x0 + 26*x1 + 18*x2 >= 14',
'5*x0 - 4*x2 >= 0',
'4*x1 - 9*x2 >= 0',
'20*x0 + 18*x2 <= 58'
]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="dish_soap_bottles", vtype=gurobi.GRB.INTEGER, lb=0)
    x1 = model.addVar(name="bottles_of_ibuprofen", vtype=gurobi.GRB.INTEGER, lb=0)
    x2 = model.addVar(name="cookies", vtype=gurobi.GRB.INTEGER, lb=0)

    # Objective function
    model.setObjective(8*x0 + 4*x1 + 6*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(11*x0 + 5*x1 + 7*x2 >= 49)
    model.addConstr(11*x0 + 5*x1 >= 33)
    model.addConstr(11*x0 + 7*x2 >= 29)
    model.addConstr(5*x1 + 7*x2 >= 49)
    model.addConstr(20*x0 + 26*x1 >= 23)
    model.addConstr(20*x0 + 18*x2 >= 16)
    model.addConstr(26*x1 + 18*x2 >= 14)
    model.addConstr(20*x0 + 26*x1 + 18*x2 >= 14)
    model.addConstr(5*x0 - 4*x2 >= 0)
    model.addConstr(4*x1 - 9*x2 >= 0)
    model.addConstr(20*x0 + 18*x2 <= 58)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("dish soap bottles: ", x0.varValue)
        print("bottles of ibuprofen: ", x1.varValue)
        print("cookies: ", x2.varValue)
    else:
        print("No solution found")

optimize_problem()
```