## Step 1: Define the symbolic representation of the variables
The variables are: 
- 'color printers' which we denote as $x_0$,
- 'lanyards' which we denote as $x_1$,
- 'mechanical pencils' which we denote as $x_2$,
- 'red highlighters' which we denote as $x_3$.

## Step 2: Translate the objective function into algebraic terms
The objective function to maximize is: $6x_0 + 1x_1 + 4x_2 + 6x_3$.

## Step 3: List all constraints in algebraic terms
1. $32x_0 + 14x_1 + 13x_2 \geq 92$
2. $32x_0 + 13x_2 + 30x_3 \geq 92$
3. $32x_0 + 14x_1 + 13x_2 \geq 65$
4. $32x_0 + 13x_2 + 30x_3 \geq 65$
5. $15x_0 + 25x_1 \geq 20$
6. $15x_2 + 30x_3 \geq 26$
7. $25x_1 + 15x_2 + 30x_3 \geq 42$
8. $15x_0 + 15x_2 + 30x_3 \geq 42$
9. $25x_1 + 15x_2 + 30x_3 \geq 35$
10. $15x_0 + 15x_2 + 30x_3 \geq 35$
11. $14x_1 + 13x_2 \leq 314$
12. $14x_1 + 30x_3 \leq 116$
13. $13x_2 + 30x_3 \leq 143$
14. $32x_0 + 14x_1 + 13x_2 \leq 321$
15. $32x_0 + 13x_2 + 30x_3 \leq 311$
16. $14x_1 + 13x_2 + 30x_3 \leq 336$
17. $32x_0 + 14x_1 + 13x_2 + 30x_3 \leq 336$
18. $25x_1 + 30x_3 \leq 62$
19. $25x_1 + 15x_2 \leq 167$
20. $15x_0 + 30x_3 \leq 127$
21. $15x_0 + 25x_1 + 15x_2 \leq 184$
22. $15x_0 + 15x_2 + 30x_3 \leq 216$
23. $25x_1 + 15x_2 + 30x_3 \leq 67$
24. $15x_0 + 25x_1 + 15x_2 + 30x_3 \leq 67$

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'color printers'), 
        ('x1', 'lanyards'), 
        ('x2', 'mechanical pencils'), 
        ('x3', 'red highlighters')
    ], 
    'objective_function': '6*x0 + 1*x1 + 4*x2 + 6*x3', 
    'constraints': [
        '32*x0 + 14*x1 + 13*x2 >= 92',
        '32*x0 + 13*x2 + 30*x3 >= 92',
        '32*x0 + 14*x1 + 13*x2 >= 65',
        '32*x0 + 13*x2 + 30*x3 >= 65',
        '15*x0 + 25*x1 >= 20',
        '15*x2 + 30*x3 >= 26',
        '25*x1 + 15*x2 + 30*x3 >= 42',
        '15*x0 + 15*x2 + 30*x3 >= 42',
        '25*x1 + 15*x2 + 30*x3 >= 35',
        '15*x0 + 15*x2 + 30*x3 >= 35',
        '14*x1 + 13*x2 <= 314',
        '14*x1 + 30*x3 <= 116',
        '13*x2 + 30*x3 <= 143',
        '32*x0 + 14*x1 + 13*x2 <= 321',
        '32*x0 + 13*x2 + 30*x3 <= 311',
        '14*x1 + 13*x2 + 30*x3 <= 336',
        '32*x0 + 14*x1 + 13*x2 + 30*x3 <= 336',
        '25*x1 + 30*x3 <= 62',
        '25*x1 + 15*x2 <= 167',
        '15*x0 + 30*x3 <= 127',
        '15*x0 + 25*x1 + 15*x2 <= 184',
        '15*x0 + 15*x2 + 30*x3 <= 216',
        '25*x1 + 15*x2 + 30*x3 <= 67',
        '15*x0 + 25*x1 + 15*x2 + 30*x3 <= 67'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # color printers
x1 = m.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # lanyards
x2 = m.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # mechanical pencils
x3 = m.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # red highlighters

# Define the objective function
m.setObjective(6 * x0 + 1 * x1 + 4 * x2 + 6 * x3, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(32 * x0 + 14 * x1 + 13 * x2 >= 92)
m.addConstr(32 * x0 + 13 * x2 + 30 * x3 >= 92)
m.addConstr(32 * x0 + 14 * x1 + 13 * x2 >= 65)
m.addConstr(32 * x0 + 13 * x2 + 30 * x3 >= 65)
m.addConstr(15 * x0 + 25 * x1 >= 20)
m.addConstr(15 * x2 + 30 * x3 >= 26)
m.addConstr(25 * x1 + 15 * x2 + 30 * x3 >= 42)
m.addConstr(15 * x0 + 15 * x2 + 30 * x3 >= 42)
m.addConstr(25 * x1 + 15 * x2 + 30 * x3 >= 35)
m.addConstr(15 * x0 + 15 * x2 + 30 * x3 >= 35)
m.addConstr(14 * x1 + 13 * x2 <= 314)
m.addConstr(14 * x1 + 30 * x3 <= 116)
m.addConstr(13 * x2 + 30 * x3 <= 143)
m.addConstr(32 * x0 + 14 * x1 + 13 * x2 <= 321)
m.addConstr(32 * x0 + 13 * x2 + 30 * x3 <= 311)
m.addConstr(14 * x1 + 13 * x2 + 30 * x3 <= 336)
m.addConstr(32 * x0 + 14 * x1 + 13 * x2 + 30 * x3 <= 336)
m.addConstr(25 * x1 + 30 * x3 <= 62)
m.addConstr(25 * x1 + 15 * x2 <= 167)
m.addConstr(15 * x0 + 30 * x3 <= 127)
m.addConstr(15 * x0 + 25 * x1 + 15 * x2 <= 184)
m.addConstr(15 * x0 + 15 * x2 + 30 * x3 <= 216)
m.addConstr(25 * x1 + 15 * x2 + 30 * x3 <= 67)
m.addConstr(15 * x0 + 25 * x1 + 15 * x2 + 30 * x3 <= 67)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Color printers: ", x0.varValue)
    print("Lanyards: ", x1.varValue)
    print("Mechanical pencils: ", x2.varValue)
    print("Red highlighters: ", x3.varValue)
else:
    print("The model is infeasible")
```