## Step 1: Define the symbolic representation of the variables
The variables are 'rubber gloves', 'packs of paper plates', 'toilet paper rolls', 'diapers' which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to maximize is $6x_0 + 4x_1 + 7x_2 + 4x_3$.

## Step 3: List the constraints in symbolic notation
The constraints given are:
- $12x_0 + 18x_2 + 23x_3 \geq 61$
- $12x_0 + 7x_1 + 23x_3 \geq 61$
- $7x_1 + 18x_2 + 23x_3 \geq 61$
- $12x_0 + 18x_2 + 23x_3 \geq 38$
- $12x_0 + 7x_1 + 23x_3 \geq 38$
- $7x_1 + 18x_2 + 23x_3 \geq 38$
- $12x_0 + 18x_2 + 23x_3 \geq 43$
- $12x_0 + 7x_1 + 23x_3 \geq 43$
- $7x_1 + 18x_2 + 23x_3 \geq 43$
- $12x_0 + 7x_1 \leq 67$
- $7x_1 + 23x_3 \leq 170$
- $18x_2 + 23x_3 \leq 91$
- $12x_0 + 23x_3 \leq 225$
- $12x_0 + 7x_1 + 18x_2 + 23x_3 \leq 225$
- $23x_0 + 12x_2 \leq 111$
- $23x_0 + 16x_1 \leq 164$
- $16x_1 + 12x_2 \leq 149$
- $23x_0 + 12x_2 + 24x_3 \leq 161$
- $23x_0 + 16x_1 + 12x_2 + 24x_3 \leq 161$
- $x_0, x_1, x_2, x_3$ are integers.

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'rubber gloves'), 
        ('x1', 'packs of paper plates'), 
        ('x2', 'toilet paper rolls'), 
        ('x3', 'diapers')
    ], 
    'objective_function': '6*x0 + 4*x1 + 7*x2 + 4*x3', 
    'constraints': [
        '12*x0 + 18*x2 + 23*x3 >= 61',
        '12*x0 + 7*x1 + 23*x3 >= 61',
        '7*x1 + 18*x2 + 23*x3 >= 61',
        '12*x0 + 18*x2 + 23*x3 >= 38',
        '12*x0 + 7*x1 + 23*x3 >= 38',
        '7*x1 + 18*x2 + 23*x3 >= 38',
        '12*x0 + 18*x2 + 23*x3 >= 43',
        '12*x0 + 7*x1 + 23*x3 >= 43',
        '7*x1 + 18*x2 + 23*x3 >= 43',
        '12*x0 + 7*x1 <= 67',
        '7*x1 + 23*x3 <= 170',
        '18*x2 + 23*x3 <= 91',
        '12*x0 + 23*x3 <= 225',
        '12*x0 + 7*x1 + 18*x2 + 23*x3 <= 225',
        '23*x0 + 12*x2 <= 111',
        '23*x0 + 16*x1 <= 164',
        '16*x1 + 12*x2 <= 149',
        '23*x0 + 12*x2 + 24*x3 <= 161',
        '23*x0 + 16*x1 + 12*x2 + 24*x3 <= 161'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="rubber gloves", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="packs of paper plates", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="toilet paper rolls", vtype=gp.GRB.INTEGER)
x3 = m.addVar(name="diapers", vtype=gp.GRB.INTEGER)

# Objective function
m.setObjective(6*x0 + 4*x1 + 7*x2 + 4*x3, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(12*x0 + 18*x2 + 23*x3 >= 61)
m.addConstr(12*x0 + 7*x1 + 23*x3 >= 61)
m.addConstr(7*x1 + 18*x2 + 23*x3 >= 61)
m.addConstr(12*x0 + 18*x2 + 23*x3 >= 38)
m.addConstr(12*x0 + 7*x1 + 23*x3 >= 38)
m.addConstr(7*x1 + 18*x2 + 23*x3 >= 38)
m.addConstr(12*x0 + 18*x2 + 23*x3 >= 43)
m.addConstr(12*x0 + 7*x1 + 23*x3 >= 43)
m.addConstr(7*x1 + 18*x2 + 23*x3 >= 43)
m.addConstr(12*x0 + 7*x1 <= 67)
m.addConstr(7*x1 + 23*x3 <= 170)
m.addConstr(18*x2 + 23*x3 <= 91)
m.addConstr(12*x0 + 23*x3 <= 225)
m.addConstr(12*x0 + 7*x1 + 18*x2 + 23*x3 <= 225)
m.addConstr(23*x0 + 12*x2 <= 111)
m.addConstr(23*x0 + 16*x1 <= 164)
m.addConstr(16*x1 + 12*x2 <= 149)
m.addConstr(23*x0 + 12*x2 + 24*x3 <= 161)
m.addConstr(23*x0 + 16*x1 + 12*x2 + 24*x3 <= 161)

# Set bounds for resources
m.addConstr(x0 <= 248/12)
m.addConstr(x1 <= 248/7)
m.addConstr(x2 <= 248/18)
m.addConstr(x3 <= 248/23)

m.addConstr(23*x0 + 12*x2 <= 164)
m.addConstr(23*x0 + 16*x1 <= 164)
m.addConstr(16*x1 + 12*x2 <= 149)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("rubber gloves: ", x0.varValue)
    print("packs of paper plates: ", x1.varValue)
    print("toilet paper rolls: ", x2.varValue)
    print("diapers: ", x3.varValue)
else:
    print("The model is infeasible")
```