## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- 'x0' for 'yellow highlighters'
- 'x1' for 'blue pens'
- 'x2' for 'mechanical pencils'
- 'x3' for 'wooden pencils'

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is: $4x_0 + 2x_1 + 6x_2 + 3x_3$

## Step 3: List all the constraints in symbolic notation
Constraints:
- $6x_0 + 2x_1 \geq 9$
- $6x_0 + 9x_3 \geq 11$
- $6x_0 + 2x_1 + 4x_2 + 9x_3 \geq 11$
- $2x_0 + 8x_3 \geq 26$
- $3x_1 + 4x_2 \geq 11$
- $2x_0 + 3x_1 + 8x_3 \geq 17$
- $3x_1 + 4x_2 + 8x_3 \geq 17$
- $2x_0 + 4x_2 + 8x_3 \geq 17$
- $2x_0 + 3x_1 + 8x_3 \geq 13$
- $3x_1 + 4x_2 + 8x_3 \geq 13$
- $2x_0 + 4x_2 + 8x_3 \geq 13$
- $2x_0 + 3x_1 + 8x_3 \geq 17$
- $3x_1 + 4x_2 + 8x_3 \geq 17$
- $2x_0 + 4x_2 + 8x_3 \geq 17$
- $2x_0 + 3x_1 + 4x_2 + 8x_3 \geq 17$
- $2x_2 + 3x_3 \geq 10$
- $2x_1 + 3x_2 \geq 12$
- $2x_0 + 2x_1 \geq 22$
- $2x_0 + 3x_2 \geq 13$
- $2x_0 + 2x_1 + 3x_2 + 3x_3 \geq 13$
- $5x_1 + 2x_2 \geq 16$
- $11x_0 + 5x_3 \geq 11$
- $5x_1 + 5x_3 \geq 13$
- $11x_0 + 2x_2 \geq 15$
- $11x_0 + 5x_1 + 2x_2 + 5x_3 \geq 15$
- $x_1 + 8x_2 \geq 8$
- $3x_0 + x_1 \geq 16$
- $3x_0 + 8x_2 \geq 15$
- $x_1 + x_3 \geq 20$
- $3x_0 + x_1 + 8x_2 + x_3 \geq 20$
- $-7x_0 + 4x_3 \geq 0$
- $2x_1 + 3x_2 \leq 63$
- $2x_0 + 3x_2 \leq 91$
- $2x_0 + 3x_3 \leq 78$
- $2x_0 + 3x_2 + 3x_3 \leq 81$
- $2x_0 + 2x_1 + 3x_2 \leq 89$
- $2x_0 + 2x_1 + 3x_3 \leq 79$
- $2x_2 + 5x_3 \leq 85$
- $5x_1 + 5x_3 \leq 62$
- $5x_1 + 2x_2 \leq 64$
- $11x_0 + 5x_3 \leq 82$
- $11x_0 + 5x_1 + 2x_2 \leq 52$
- $11x_0 + 5x_1 + 5x_3 \leq 73$
- $x_1 + 8x_2 \leq 72$
- $3x_0 + x_3 \leq 45$
- $3x_0 + 8x_2 \leq 61$

## Step 4: Define the problem in Gurobi
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="yellow_highlighters", vtype=gp.GRB.INTEGER)
x1 = m.addVar(name="blue_pens", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="mechanical_pencils", vtype=gp.GRB.INTEGER)
x3 = m.addVar(name="wooden_pencils", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(4 * x0 + 2 * x1 + 6 * x2 + 3 * x3, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(6 * x0 + 2 * x1 >= 9)
m.addConstr(6 * x0 + 9 * x3 >= 11)
m.addConstr(6 * x0 + 2 * x1 + 4 * x2 + 9 * x3 >= 11)
m.addConstr(2 * x0 + 8 * x3 >= 26)
m.addConstr(3 * x1 + 4 * x2 >= 11)
m.addConstr(2 * x0 + 3 * x1 + 8 * x3 >= 17)
m.addConstr(3 * x1 + 4 * x2 + 8 * x3 >= 17)
m.addConstr(2 * x0 + 4 * x2 + 8 * x3 >= 17)
m.addConstr(2 * x0 + 3 * x1 + 8 * x3 >= 13)
m.addConstr(3 * x1 + 4 * x2 + 8 * x3 >= 13)
m.addConstr(2 * x0 + 4 * x2 + 8 * x3 >= 13)
m.addConstr(2 * x0 + 3 * x1 + 8 * x3 >= 17)
m.addConstr(3 * x1 + 4 * x2 + 8 * x3 >= 17)
m.addConstr(2 * x0 + 4 * x2 + 8 * x3 >= 17)
m.addConstr(2 * x0 + 3 * x1 + 4 * x2 + 8 * x3 >= 17)
m.addConstr(2 * x2 + 3 * x3 >= 10)
m.addConstr(2 * x1 + 3 * x2 >= 12)
m.addConstr(2 * x0 + 2 * x1 >= 22)
m.addConstr(2 * x0 + 3 * x2 >= 13)
m.addConstr(2 * x0 + 2 * x1 + 3 * x2 + 3 * x3 >= 13)
m.addConstr(5 * x1 + 2 * x2 >= 16)
m.addConstr(11 * x0 + 5 * x3 >= 11)
m.addConstr(5 * x1 + 5 * x3 >= 13)
m.addConstr(11 * x0 + 2 * x2 >= 15)
m.addConstr(11 * x0 + 5 * x1 + 2 * x2 + 5 * x3 >= 15)
m.addConstr(x1 + 8 * x2 >= 8)
m.addConstr(3 * x0 + x1 >= 16)
m.addConstr(3 * x0 + 8 * x2 >= 15)
m.addConstr(x1 + x3 >= 20)
m.addConstr(3 * x0 + x1 + 8 * x2 + x3 >= 20)
m.addConstr(-7 * x0 + 4 * x3 >= 0)
m.addConstr(2 * x1 + 3 * x2 <= 63)
m.addConstr(2 * x0 + 3 * x2 <= 91)
m.addConstr(2 * x0 + 3 * x3 <= 78)
m.addConstr(2 * x0 + 3 * x2 + 3 * x3 <= 81)
m.addConstr(2 * x0 + 2 * x1 + 3 * x2 <= 89)
m.addConstr(2 * x0 + 2 * x1 + 3 * x3 <= 79)
m.addConstr(2 * x2 + 5 * x3 <= 85)
m.addConstr(5 * x1 + 5 * x3 <= 62)
m.addConstr(5 * x1 + 2 * x2 <= 64)
m.addConstr(11 * x0 + 5 * x3 <= 82)
m.addConstr(11 * x0 + 5 * x1 + 2 * x2 <= 52)
m.addConstr(11 * x0 + 5 * x1 + 5 * x3 <= 73)
m.addConstr(x1 + 8 * x2 <= 72)
m.addConstr(3 * x0 + x3 <= 45)
m.addConstr(3 * x0 + 8 * x2 <= 61)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Yellow Highlighters: ", x0.varValue)
    print("Blue Pens: ", x1.varValue)
    print("Mechanical Pencils: ", x2.varValue)
    print("Wooden Pencils: ", x3.varValue)
else:
    print("The model is infeasible")
```

### Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'yellow highlighters'),
        ('x1', 'blue pens'),
        ('x2', 'mechanical pencils'),
        ('x3', 'wooden pencils')
    ],
    'objective_function': '4*x0 + 2*x1 + 6*x2 + 3*x3',
    'constraints': [
        '6*x0 + 2*x1 >= 9',
        '6*x0 + 9*x3 >= 11',
        '6*x0 + 2*x1 + 4*x2 + 9*x3 >= 11',
        '2*x0 + 8*x3 >= 26',
        '3*x1 + 4*x2 >= 11',
        '2*x0 + 3*x1 + 8*x3 >= 17',
        '3*x1 + 4*x2 + 8*x3 >= 17',
        '2*x0 + 4*x2 + 8*x3 >= 17',
        '2*x0 + 3*x1 + 8*x3 >= 13',
        '3*x1 + 4*x2 + 8*x3 >= 13',
        '2*x0 + 4*x2 + 8*x3 >= 13',
        '2*x0 + 3*x1 + 8*x3 >= 17',
        '3*x1 + 4*x2 + 8*x3 >= 17',
        '2*x0 + 4*x2 + 8*x3 >= 17',
        '2*x0 + 3*x1 + 4*x2 + 8*x3 >= 17',
        '2*x2 + 3*x3 >= 10',
        '2*x1 + 3*x2 >= 12',
        '2*x0 + 2*x1 >= 22',
        '2*x0 + 3*x2 >= 13',
        '2*x0 + 2*x1 + 3*x2 + 3*x3 >= 13',
        '5*x1 + 2*x2 >= 16',
        '11*x0 + 5*x3 >= 11',
        '5*x1 + 5*x3 >= 13',
        '11*x0 + 2*x2 >= 15',
        '11*x0 + 5*x1 + 2*x2 + 5*x3 >= 15',
        'x1 + 8*x2 >= 8',
        '3*x0 + x1 >= 16',
        '3*x0 + 8*x2 >= 15',
        'x1 + x3 >= 20',
        '3*x0 + x1 + 8*x2 + x3 >= 20',
        '-7*x0 + 4*x3 >= 0',
        '2*x1 + 3*x2 <= 63',
        '2*x0 + 3*x2 <= 91',
        '2*x0 + 3*x3 <= 78',
        '2*x0 + 3*x2 + 3*x3 <= 81',
        '2*x0 + 2*x1 + 3*x2 <= 89',
        '2*x0 + 2*x1 + 3*x3 <= 79',
        '2*x2 + 5*x3 <= 85',
        '5*x1 + 5*x3 <= 62',
        '5*x1 + 2*x2 <= 64',
        '11*x0 + 5*x3 <= 82',
        '11*x0 + 5*x1 + 2*x2 <= 52',
        '11*x0 + 5*x1 + 5*x3 <= 73',
        'x1 + 8*x2 <= 72',
        '3*x0 + x3 <= 45',
        '3*x0 + 8*x2 <= 61'
    ]
}
```