## Step 1: Define the symbolic representation of the variables
The variables are 'yellow highlighters', 'paper clips', 'packs of paper', and 'manila envelopes'. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5x_0 + 8x_1 + 4x_2 + 2x_3$.

## Step 3: List all the constraints in symbolic notation
1. $6x_1 + 5x_3 \geq 23$
2. $9x_0 + 6x_1 \geq 17$
3. $6x_1 + 7x_2 \geq 30$
4. $9x_0 + 7x_2 \geq 25$
5. $9x_0 + 6x_1 + 7x_2 + 5x_3 \geq 25$
6. $10x_1 + 2x_2 \geq 16$
7. $8x_0 + 10x_1 \geq 15$
8. $2x_2 + 8x_3 \geq 10$
9. $10x_1 + 8x_3 \geq 14$
10. $8x_0 + 2x_2 \geq 24$
11. $8x_0 + 10x_1 + 2x_2 + 8x_3 \geq 24$
12. $3x_1 - x_2 \geq 0$
13. $4x_0 - x_1 \geq 0$
14. $6x_1 + 7x_2 \leq 105$
15. $6x_1 + 7x_2 + 5x_3 \leq 126$
16. $9x_0 + 6x_1 + 7x_2 \leq 59$
17. $9x_0 + 7x_2 + 5x_3 \leq 61$
18. $8x_0 + 8x_3 \leq 70$
19. $8x_0 + 10x_1 + 2x_2 \leq 72$
20. $10x_1 + 2x_2 + 8x_3 \leq 79$

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'yellow highlighters'), 
        ('x1', 'paper clips'), 
        ('x2', 'packs of paper'), 
        ('x3', 'manila envelopes')
    ], 
    'objective_function': '5*x0 + 8*x1 + 4*x2 + 2*x3', 
    'constraints': [
        '6*x1 + 5*x3 >= 23',
        '9*x0 + 6*x1 >= 17',
        '6*x1 + 7*x2 >= 30',
        '9*x0 + 7*x2 >= 25',
        '9*x0 + 6*x1 + 7*x2 + 5*x3 >= 25',
        '10*x1 + 2*x2 >= 16',
        '8*x0 + 10*x1 >= 15',
        '2*x2 + 8*x3 >= 10',
        '10*x1 + 8*x3 >= 14',
        '8*x0 + 2*x2 >= 24',
        '8*x0 + 10*x1 + 2*x2 + 8*x3 >= 24',
        '3*x1 - x2 >= 0',
        '4*x0 - x1 >= 0',
        '6*x1 + 7*x2 <= 105',
        '6*x1 + 7*x2 + 5*x3 <= 126',
        '9*x0 + 6*x1 + 7*x2 <= 59',
        '9*x0 + 7*x2 + 5*x3 <= 61',
        '8*x0 + 8*x3 <= 70',
        '8*x0 + 10*x1 + 2*x2 <= 72',
        '10*x1 + 2*x2 + 8*x3 <= 79'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name="yellow_highlighters", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="paper_clips", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="packs_of_paper", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="manila_envelopes", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(5*x0 + 8*x1 + 4*x2 + 2*x3, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(6*x1 + 5*x3 >= 23)
m.addConstr(9*x0 + 6*x1 >= 17)
m.addConstr(6*x1 + 7*x2 >= 30)
m.addConstr(9*x0 + 7*x2 >= 25)
m.addConstr(9*x0 + 6*x1 + 7*x2 + 5*x3 >= 25)
m.addConstr(10*x1 + 2*x2 >= 16)
m.addConstr(8*x0 + 10*x1 >= 15)
m.addConstr(2*x2 + 8*x3 >= 10)
m.addConstr(10*x1 + 8*x3 >= 14)
m.addConstr(8*x0 + 2*x2 >= 24)
m.addConstr(8*x0 + 10*x1 + 2*x2 + 8*x3 >= 24)
m.addConstr(3*x1 - x2 >= 0)
m.addConstr(4*x0 - x1 >= 0)
m.addConstr(6*x1 + 7*x2 <= 105)
m.addConstr(6*x1 + 7*x2 + 5*x3 <= 126)
m.addConstr(9*x0 + 6*x1 + 7*x2 <= 59)
m.addConstr(9*x0 + 7*x2 + 5*x3 <= 61)
m.addConstr(8*x0 + 8*x3 <= 70)
m.addConstr(8*x0 + 10*x1 + 2*x2 <= 72)
m.addConstr(10*x1 + 2*x2 + 8*x3 <= 79)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Yellow Highlighters: ", x0.varValue)
    print("Paper Clips: ", x1.varValue)
    print("Packs of Paper: ", x2.varValue)
    print("Manila Envelopes: ", x3.varValue)
else:
    print("The model is infeasible")
```