## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are 'blue highlighters', 'usb flash drives', and 'hole punches', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $5.14x_0 + 7.99x_1 + 3.29x_2$.

## 3: List the constraints in symbolic notation
1. $12x_0 + 11x_1 \geq 22$
2. $11x_1 + 3x_2 \geq 29$
3. $12x_0 + 11x_1 + 3x_2 \geq 29$
4. $4x_1 + 6x_2 \geq 45$
5. $12x_0 + 4x_1 \geq 50$
6. $12x_0 + 4x_1 + 6x_2 \geq 50$
7. $11x_1 + 3x_2 \geq 24$
8. $5x_0 + 11x_1 \geq 24$
9. $5x_0 + 11x_1 + 3x_2 \geq 34$
10. $18x_0 + 8x_2 \geq 46$
11. $13x_1 + 8x_2 \geq 47$
12. $18x_0 + 13x_1 + 8x_2 \geq 47$
13. $-3x_0 + 2x_1 \geq 0$
14. $12x_0 + 4x_1 \leq 116$
15. $12x_0 + 4x_1 + 6x_2 \leq 82$
16. $5x_0 + 11x_1 + 3x_2 \leq 49$
17. $18x_0 + 13x_1 \leq 128$
18. $18x_0 + 8x_2 \leq 139$
19. $x_0, x_1, x_2 \geq 0$ and are integers.

## 4: Write down the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'blue highlighters'), ('x1', 'usb flash drives'), ('x2', 'hole punches')],
'objective_function': '5.14*x0 + 7.99*x1 + 3.29*x2',
'constraints': [
'12*x0 + 11*x1 >= 22',
'11*x1 + 3*x2 >= 29',
'12*x0 + 11*x1 + 3*x2 >= 29',
'4*x1 + 6*x2 >= 45',
'12*x0 + 4*x1 >= 50',
'12*x0 + 4*x1 + 6*x2 >= 50',
'11*x1 + 3*x2 >= 24',
'5*x0 + 11*x1 >= 24',
'5*x0 + 11*x1 + 3*x2 >= 34',
'18*x0 + 8*x2 >= 46',
'13*x1 + 8*x2 >= 47',
'18*x0 + 13*x1 + 8*x2 >= 47',
'-3*x0 + 2*x1 >= 0',
'12*x0 + 4*x1 <= 116',
'12*x0 + 4*x1 + 6*x2 <= 82',
'5*x0 + 11*x1 + 3*x2 <= 49',
'18*x0 + 13*x1 <= 128',
'18*x0 + 8*x2 <= 139'
]
}
```

## 5: Implement the problem in Gurobi
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="blue_highlighters", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="usb_flash_drives", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="hole_punches", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(5.14*x0 + 7.99*x1 + 3.29*x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(12*x0 + 11*x1 >= 22)
m.addConstr(11*x1 + 3*x2 >= 29)
m.addConstr(12*x0 + 11*x1 + 3*x2 >= 29)
m.addConstr(4*x1 + 6*x2 >= 45)
m.addConstr(12*x0 + 4*x1 >= 50)
m.addConstr(12*x0 + 4*x1 + 6*x2 >= 50)
m.addConstr(11*x1 + 3*x2 >= 24)
m.addConstr(5*x0 + 11*x1 >= 24)
m.addConstr(5*x0 + 11*x1 + 3*x2 >= 34)
m.addConstr(18*x0 + 8*x2 >= 46)
m.addConstr(13*x1 + 8*x2 >= 47)
m.addConstr(18*x0 + 13*x1 + 8*x2 >= 47)
m.addConstr(-3*x0 + 2*x1 >= 0)
m.addConstr(12*x0 + 4*x1 <= 116)
m.addConstr(12*x0 + 4*x1 + 6*x2 <= 82)
m.addConstr(5*x0 + 11*x1 + 3*x2 <= 49)
m.addConstr(18*x0 + 13*x1 <= 128)
m.addConstr(18*x0 + 8*x2 <= 139)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Blue highlighters: ", x0.varValue)
    print("USB flash drives: ", x1.varValue)
    print("Hole punches: ", x2.varValue)
else:
    print("The model is infeasible")
```