## Step 1: Define the symbolic representation of the variables
The variables are 'rubber gloves', 'dish soap bottles', 'toilet paper rolls', and 'cookies', which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $5x_1 + 2x_2 + 7x_3 + 6x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $15.84x_1 \geq 0$ ( implicit, as $x_1$ is non-negative)
- $3.04x_2 \geq 0$ ( implicit, as $x_2$ is non-negative)
- $9.19x_3 \geq 0$ ( implicit, as $x_3$ is non-negative)
- $26.5x_4 \geq 0$ ( implicit, as $x_4$ is non-negative)
- $15.84x_1 + 9.19x_3 \geq 127$
- $3.04x_2 + 9.19x_3 \geq 84$
- $9.19x_3 + 26.5x_4 \geq 71$
- $15.84x_1 + 3.04x_2 + 9.19x_3 \geq 122$
- $15.84x_1 + 3.04x_2 + 26.5x_4 \geq 122$
- $15.84x_1 + 9.19x_3 + 26.5x_4 \geq 122$
- $15.84x_1 + 3.04x_2 + 9.19x_3 \geq 133$
- $15.84x_1 + 3.04x_2 + 26.5x_4 \geq 133$
- $15.84x_1 + 9.19x_3 + 26.5x_4 \geq 133$
- $15.84x_1 + 3.04x_2 + 9.19x_3 \geq 105$
- $15.84x_1 + 3.04x_2 + 26.5x_4 \geq 105$
- $15.84x_1 + 9.19x_3 + 26.5x_4 \geq 105$
- $15.84x_1 + 3.04x_2 \leq 511$
- $9.19x_3 + 26.5x_4 \leq 424$
- $3.04x_2 + 26.5x_4 \leq 569$
- $15.84x_1 + 9.19x_3 \leq 154$
- $15.84x_1 + 3.04x_2 + 9.19x_3 + 26.5x_4 \leq 154$

## 4: Convert the problem into Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name="rubber_gloves", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="dish_soap_bottles", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="toilet_paper_rolls", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="cookies", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(5*x1 + 2*x2 + 7*x3 + 6*x4, gurobi.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(15.84*x1 + 9.19*x3 >= 127)
m.addConstr(3.04*x2 + 9.19*x3 >= 84)
m.addConstr(9.19*x3 + 26.5*x4 >= 71)
m.addConstr(15.84*x1 + 3.04*x2 + 9.19*x3 >= 122)
m.addConstr(15.84*x1 + 3.04*x2 + 26.5*x4 >= 122)
m.addConstr(15.84*x1 + 9.19*x3 + 26.5*x4 >= 122)
m.addConstr(15.84*x1 + 3.04*x2 + 9.19*x3 >= 133)
m.addConstr(15.84*x1 + 3.04*x2 + 26.5*x4 >= 133)
m.addConstr(15.84*x1 + 9.19*x3 + 26.5*x4 >= 133)
m.addConstr(15.84*x1 + 3.04*x2 + 9.19*x3 >= 105)
m.addConstr(15.84*x1 + 3.04*x2 + 26.5*x4 >= 105)
m.addConstr(15.84*x1 + 9.19*x3 + 26.5*x4 >= 105)
m.addConstr(15.84*x1 + 3.04*x2 <= 511)
m.addConstr(9.19*x3 + 26.5*x4 <= 424)
m.addConstr(3.04*x2 + 26.5*x4 <= 569)
m.addConstr(15.84*x1 + 9.19*x3 <= 154)
m.addConstr(15.84*x1 + 3.04*x2 + 9.19*x3 + 26.5*x4 <= 154)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Rubber Gloves: ", x1.varValue)
    print("Dish Soap Bottles: ", x2.varValue)
    print("Toilet Paper Rolls: ", x3.varValue)
    print("Cookies: ", x4.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'rubber gloves'), 
        ('x2', 'dish soap bottles'), 
        ('x3', 'toilet paper rolls'), 
        ('x4', 'cookies')
    ], 
    'objective_function': '5*x1 + 2*x2 + 7*x3 + 6*x4', 
    'constraints': [
        '15.84*x1 + 9.19*x3 >= 127',
        '3.04*x2 + 9.19*x3 >= 84',
        '9.19*x3 + 26.5*x4 >= 71',
        '15.84*x1 + 3.04*x2 + 9.19*x3 >= 122',
        '15.84*x1 + 3.04*x2 + 26.5*x4 >= 122',
        '15.84*x1 + 9.19*x3 + 26.5*x4 >= 122',
        '15.84*x1 + 3.04*x2 + 9.19*x3 >= 133',
        '15.84*x1 + 3.04*x2 + 26.5*x4 >= 133',
        '15.84*x1 + 9.19*x3 + 26.5*x4 >= 133',
        '15.84*x1 + 3.04*x2 + 9.19*x3 >= 105',
        '15.84*x1 + 3.04*x2 + 26.5*x4 >= 105',
        '15.84*x1 + 9.19*x3 + 26.5*x4 >= 105',
        '15.84*x1 + 3.04*x2 <= 511',
        '9.19*x3 + 26.5*x4 <= 424',
        '3.04*x2 + 26.5*x4 <= 569',
        '15.84*x1 + 9.19*x3 <= 154',
        '15.84*x1 + 3.04*x2 + 9.19*x3 + 26.5*x4 <= 154'
    ]
}
```