## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic representation of the problem, including the variables, objective function, and constraints.

## Step 2: Identify the variables and their corresponding symbolic notation
The variables are 'rubber gloves', 'paper towel rolls', and 'diapers', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is $2x_0 + 3x_1 + 5x_2$.

## Step 4: List the constraints in symbolic notation
The constraints are:
- $2x_0 + 10x_2 \geq 30$
- $2x_0 + 7x_1 \geq 35$
- $x_0 + 12x_2 \geq 10$
- $6x_0 - 9x_1 \geq 0$
- $2x_0 + 10x_2 \leq 154$
- $7x_1 + 10x_2 \leq 87$
- $2x_0 + 7x_1 + 10x_2 \leq 87$
- $x_0 + 12x_2 \leq 62$
- $x_0 + 15x_1 \leq 28$
- $x_0 + 15x_1 + 12x_2 \leq 28$
- $x_0, x_1, x_2$ are integers.

## 5: Convert the problem into a Gurobi model
Now, let's convert this problem into a Gurobi model.

## 6: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="rubber_gloves", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="paper_towel_rolls", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="diapers", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(2*x0 + 3*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x0 + 10*x2 >= 30)
m.addConstr(2*x0 + 7*x1 >= 35)
m.addConstr(x0 + 12*x2 >= 10)
m.addConstr(6*x0 - 9*x1 >= 0)
m.addConstr(2*x0 + 10*x2 <= 154)
m.addConstr(7*x1 + 10*x2 <= 87)
m.addConstr(2*x0 + 7*x1 + 10*x2 <= 87)
m.addConstr(x0 + 12*x2 <= 62)
m.addConstr(x0 + 15*x1 <= 28)
m.addConstr(x0 + 15*x1 + 12*x2 <= 28)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("rubber gloves: ", x0.varValue)
    print("paper towel rolls: ", x1.varValue)
    print("diapers: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'rubber gloves'), ('x1', 'paper towel rolls'), ('x2', 'diapers')],
    'objective_function': '2*x0 + 3*x1 + 5*x2',
    'constraints': [
        '2*x0 + 10*x2 >= 30',
        '2*x0 + 7*x1 >= 35',
        'x0 + 12*x2 >= 10',
        '6*x0 - 9*x1 >= 0',
        '2*x0 + 10*x2 <= 154',
        '7*x1 + 10*x2 <= 87',
        '2*x0 + 7*x1 + 10*x2 <= 87',
        'x0 + 12*x2 <= 62',
        'x0 + 15*x1 <= 28',
        'x0 + 15*x1 + 12*x2 <= 28'
    ]
}
```