## Step 1: Define the symbolic representation of the variables
The variables are 'red pens', 'postage stamps', 'lanyards', 'usb flash drives', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $2 \times (\text{red pens}) + 8 \times (\text{postage stamps}) + 6 \times (\text{lanyards}) + 6 \times (\text{usb flash drives})$. In symbolic terms, this is $2x_0 + 8x_1 + 6x_2 + 6x_3$.

## 3: List the constraints in symbolic notation
1. $\text{red pens} \geq 0$ and $\text{postage stamps} \geq 0$ and $\text{lanyards} \geq 0$ and $\text{usb flash drives} \geq 0$ (non-negativity constraints are implicit in integer constraints)
2. $11x_0 + 14x_1 + 11x_2 + 5x_3 \leq 253$ (total cost constraint)
3. $13x_0 + 4x_1 + 18x_2 + 3x_3 \leq 79$ (total workplace safety impact constraint)
4. $11x_0 \geq 45 - 5x_3$ or $11x_0 + 5x_3 \geq 45$ (minimum spend on red pens and usb flash drives)
5. $11x_2 + 5x_3 \geq 33$ (minimum spend on lanyards and usb flash drives)
6. $11x_0 + 14x_1 \geq 35$ (minimum spend on red pens and postage stamps)
7. $11x_0 + 14x_1 + 11x_2 + 5x_3 \geq 35$ (minimum total spend)
8. $4x_1 + 18x_2 \geq 11$ (minimum workplace safety impact from postage stamps and lanyards)
9. $13x_0 + 18x_2 \geq 8$ (minimum workplace safety impact from red pens and lanyards)
10. $13x_0 + 4x_1 \geq 15$ (minimum workplace safety impact from red pens and postage stamps)
11. $13x_0 + 4x_1 + 18x_2 \geq 15$ (minimum workplace safety impact from red pens, postage stamps, and lanyards)
12. $13x_0 + 4x_1 + 18x_2 + 3x_3 \geq 15$ (minimum total workplace safety impact)
13. $-8x_1 + 4x_3 \geq 0$ (constraint on postage stamps and usb flash drives)
14. $-4x_0 + 4x_2 \geq 0$ (constraint on red pens and lanyards)
15. $11x_0 + 14x_1 \leq 160$ (maximum spend on red pens and postage stamps)
16. $14x_1 + 11x_2 \leq 237$ (maximum spend on postage stamps and lanyards)
17. $13x_0 + 4x_1 \leq 34$ (maximum workplace safety impact from red pens and postage stamps)
18. $4x_1 + 3x_3 \leq 32$ (maximum workplace safety impact from postage stamps and usb flash drives)
19. $13x_0 + 3x_3 \leq 68$ (maximum workplace safety impact from red pens and usb flash drives)
20. $4x_1 + 18x_2 \leq 30$ (maximum workplace safety impact from postage stamps and lanyards)
21. $13x_0 + 4x_1 + 3x_3 \leq 59$ (maximum workplace safety impact from red pens, postage stamps, and usb flash drives)
22. $13x_0 + 4x_1 + 18x_2 \leq 25$ (maximum workplace safety impact from red pens, postage stamps, and lanyards)

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'red pens'), ('x1', 'postage stamps'), ('x2', 'lanyards'), ('x3', 'usb flash drives')],
    'objective_function': '2*x0 + 8*x1 + 6*x2 + 6*x3',
    'constraints': [
        '11*x0 + 14*x1 + 11*x2 + 5*x3 <= 253',
        '13*x0 + 4*x1 + 18*x2 + 3*x3 <= 79',
        '11*x0 + 5*x3 >= 45',
        '11*x2 + 5*x3 >= 33',
        '11*x0 + 14*x1 >= 35',
        '11*x0 + 14*x1 + 11*x2 + 5*x3 >= 35',
        '4*x1 + 18*x2 >= 11',
        '13*x0 + 18*x2 >= 8',
        '13*x0 + 4*x1 >= 15',
        '13*x0 + 4*x1 + 18*x2 >= 15',
        '13*x0 + 4*x1 + 18*x2 + 3*x3 >= 15',
        '-8*x1 + 4*x3 >= 0',
        '-4*x0 + 4*x2 >= 0',
        '11*x0 + 14*x1 <= 160',
        '14*x1 + 11*x2 <= 237',
        '13*x0 + 4*x1 <= 34',
        '4*x1 + 3*x3 <= 32',
        '13*x0 + 3*x3 <= 68',
        '4*x1 + 18*x2 <= 30',
        '13*x0 + 4*x1 + 3*x3 <= 59',
        '13*x0 + 4*x1 + 18*x2 <= 25'
    ]
}
```

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

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

# Define the variables
x0 = model.addVar(name="red_pens", vtype=gurobi.GRB.INTEGER)
x1 = model.addVar(name="postage_stamps", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="lanyards", vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name="usb_flash_drives", vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(2*x0 + 8*x1 + 6*x2 + 6*x3, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(11*x0 + 14*x1 + 11*x2 + 5*x3 <= 253)
model.addConstr(13*x0 + 4*x1 + 18*x2 + 3*x3 <= 79)
model.addConstr(11*x0 + 5*x3 >= 45)
model.addConstr(11*x2 + 5*x3 >= 33)
model.addConstr(11*x0 + 14*x1 >= 35)
model.addConstr(11*x0 + 14*x1 + 11*x2 + 5*x3 >= 35)
model.addConstr(4*x1 + 18*x2 >= 11)
model.addConstr(13*x0 + 18*x2 >= 8)
model.addConstr(13*x0 + 4*x1 >= 15)
model.addConstr(13*x0 + 4*x1 + 18*x2 >= 15)
model.addConstr(13*x0 + 4*x1 + 18*x2 + 3*x3 >= 15)
model.addConstr(-8*x1 + 4*x3 >= 0)
model.addConstr(-4*x0 + 4*x2 >= 0)
model.addConstr(11*x0 + 14*x1 <= 160)
model.addConstr(14*x1 + 11*x2 <= 237)
model.addConstr(13*x0 + 4*x1 <= 34)
model.addConstr(4*x1 + 3*x3 <= 32)
model.addConstr(13*x0 + 3*x3 <= 68)
model.addConstr(4*x1 + 18*x2 <= 30)
model.addConstr(13*x0 + 4*x1 + 3*x3 <= 59)
model.addConstr(13*x0 + 4*x1 + 18*x2 <= 25)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Red pens: ", x0.varValue)
    print("Postage stamps: ", x1.varValue)
    print("Lanyards: ", x2.varValue)
    print("USB flash drives: ", x3.varValue)
else:
    print("The model is infeasible")
```