## Step 1: Define the variables and their corresponding natural language objects
The variables and their corresponding natural language objects are:
- x1: lanyards
- x2: mechanical pencils
- x3: red pens
- x4: blue pens
- x5: monochrome printers
- x6: packs of paper
- x7: black pens

## Step 2: Formulate the objective function
The objective function to maximize is: 
4 * lanyards + 5 * mechanical pencils + 5 * red pens + 6 * blue pens + 3 * monochrome printers + 7 * packs of paper + 4 * black pens
In symbolic notation, this is: 
4*x1 + 5*x2 + 5*x3 + 6*x4 + 3*x5 + 7*x6 + 4*x7

## Step 3: List the constraints
The constraints are:
1. 6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 175
2. 6*x1 + 9*x2 >= 15
3. 9*x3 + 10*x4 >= 16
4. 9*x2 + 7*x7 >= 25
5. 6*x1 + 15*x6 >= 12
6. 9*x2 + 9*x3 >= 23
7. 15*x6 + 7*x7 >= 14
8. 6*x1 + 7*x7 >= 25
9. 10*x4 + 4*x5 >= 12
10. 9*x3 + 15*x6 >= 10
11. 6*x1 + 10*x4 >= 16
12. 9*x2 + 4*x5 >= 10
13. 4*x5 + 15*x6 >= 17
14. 10*x4 + 15*x6 >= 19
15. 4*x5 + 7*x7 >= 12
16. 9*x3 + 10*x4 + 15*x6 >= 25
17. 9*x3 + 4*x5 + 7*x7 >= 25
18. 6*x1 + 4*x5 + 7*x7 >= 25
19. 6*x1 + 9*x2 + 15*x6 >= 25
20. 9*x3 + 10*x4 + 15*x6 >= 22
21. 9*x3 + 4*x5 + 7*x7 >= 22
22. 6*x1 + 4*x5 + 7*x7 >= 22
23. 6*x1 + 9*x2 + 15*x6 >= 22
24. 9*x3 + 10*x4 + 15*x6 >= 13
25. 9*x3 + 4*x5 + 7*x7 >= 13
26. 6*x1 + 4*x5 + 7*x7 >= 13
27. 6*x1 + 9*x2 + 15*x6 >= 13
28. 9*x3 + 10*x4 + 15*x6 >= 16
29. 9*x3 + 4*x5 + 7*x7 >= 16
30. 6*x1 + 4*x5 + 7*x7 >= 16
31. 6*x1 + 9*x2 + 15*x6 >= 16
32. -4*x4 + 10*x7 >= 0
33. 6*x1 + 4*x5 <= 40
34. 9*x2 + 10*x4 <= 136
35. 4*x5 + 15*x6 <= 34
36. 6*x1 + 10*x4 <= 52
37. 9*x3 + 7*x7 <= 141
38. 15*x6 + 7*x7 <= 108
39. 9*x3 + 4*x5 <= 104
40. 9*x2 + 9*x3 <= 53
41. 9*x3 + 15*x6 <= 64
42. 9*x2 + 15*x6 <= 158
43. 4*x5 + 7*x7 <= 61
44. 10*x4 + 15*x6 <= 35
45. 6*x1 + 15*x6 <= 116
46. 6*x1 + 4*x5 + 15*x6 <= 120
47. 6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 120

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'lanyards'),
        ('x2', 'mechanical pencils'),
        ('x3', 'red pens'),
        ('x4', 'blue pens'),
        ('x5', 'monochrome printers'),
        ('x6', 'packs of paper'),
        ('x7', 'black pens')
    ],
    'objective_function': '4*x1 + 5*x2 + 5*x3 + 6*x4 + 3*x5 + 7*x6 + 4*x7',
    'constraints': [
        '6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 175',
        '6*x1 + 9*x2 >= 15',
        '9*x3 + 10*x4 >= 16',
        '9*x2 + 7*x7 >= 25',
        '6*x1 + 15*x6 >= 12',
        '9*x2 + 9*x3 >= 23',
        '15*x6 + 7*x7 >= 14',
        '6*x1 + 7*x7 >= 25',
        '10*x4 + 4*x5 >= 12',
        '9*x3 + 15*x6 >= 10',
        '6*x1 + 10*x4 >= 16',
        '9*x2 + 4*x5 >= 10',
        '4*x5 + 15*x6 >= 17',
        '10*x4 + 15*x6 >= 19',
        '4*x5 + 7*x7 >= 12',
        '9*x3 + 10*x4 + 15*x6 >= 25',
        '9*x3 + 4*x5 + 7*x7 >= 25',
        '6*x1 + 4*x5 + 7*x7 >= 25',
        '6*x1 + 9*x2 + 15*x6 >= 25',
        '9*x3 + 10*x4 + 15*x6 >= 22',
        '9*x3 + 4*x5 + 7*x7 >= 22',
        '6*x1 + 4*x5 + 7*x7 >= 22',
        '6*x1 + 9*x2 + 15*x6 >= 22',
        '9*x3 + 10*x4 + 15*x6 >= 13',
        '9*x3 + 4*x5 + 7*x7 >= 13',
        '6*x1 + 4*x5 + 7*x7 >= 13',
        '6*x1 + 9*x2 + 15*x6 >= 13',
        '9*x3 + 10*x4 + 15*x6 >= 16',
        '9*x3 + 4*x5 + 7*x7 >= 16',
        '6*x1 + 4*x5 + 7*x7 >= 16',
        '6*x1 + 9*x2 + 15*x6 >= 16',
        '-4*x4 + 10*x7 >= 0',
        '6*x1 + 4*x5 <= 40',
        '9*x2 + 10*x4 <= 136',
        '4*x5 + 15*x6 <= 34',
        '6*x1 + 10*x4 <= 52',
        '9*x3 + 7*x7 <= 141',
        '15*x6 + 7*x7 <= 108',
        '9*x3 + 4*x5 <= 104',
        '9*x2 + 9*x3 <= 53',
        '9*x3 + 15*x6 <= 64',
        '9*x2 + 15*x6 <= 158',
        '4*x5 + 7*x7 <= 61',
        '10*x4 + 15*x6 <= 35',
        '6*x1 + 15*x6 <= 116',
        '6*x1 + 4*x5 + 15*x6 <= 120',
        '6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 120'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name="lanyards", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="mechanical_pencils", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="red_pens", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="blue_pens", vtype=gurobi.GRB.INTEGER)
x5 = m.addVar(name="monochrome_printers", vtype=gurobi.GRB.INTEGER)
x6 = m.addVar(name="packs_of_paper", vtype=gurobi.GRB.INTEGER)
x7 = m.addVar(name="black_pens", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(4*x1 + 5*x2 + 5*x3 + 6*x4 + 3*x5 + 7*x6 + 4*x7, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 175)
m.addConstr(6*x1 + 9*x2 >= 15)
m.addConstr(9*x3 + 10*x4 >= 16)
m.addConstr(9*x2 + 7*x7 >= 25)
m.addConstr(6*x1 + 15*x6 >= 12)
m.addConstr(9*x2 + 9*x3 >= 23)
m.addConstr(15*x6 + 7*x7 >= 14)
m.addConstr(6*x1 + 7*x7 >= 25)
m.addConstr(10*x4 + 4*x5 >= 12)
m.addConstr(9*x3 + 15*x6 >= 10)
m.addConstr(6*x1 + 10*x4 >= 16)
m.addConstr(9*x2 + 4*x5 >= 10)
m.addConstr(4*x5 + 15*x6 >= 17)
m.addConstr(10*x4 + 15*x6 >= 19)
m.addConstr(4*x5 + 7*x7 >= 12)
m.addConstr(9*x3 + 10*x4 + 15*x6 >= 25)
m.addConstr(9*x3 + 4*x5 + 7*x7 >= 25)
m.addConstr(6*x1 + 4*x5 + 7*x7 >= 25)
m.addConstr(6*x1 + 9*x2 + 15*x6 >= 25)
m.addConstr(9*x3 + 10*x4 + 15*x6 >= 22)
m.addConstr(9*x3 + 4*x5 + 7*x7 >= 22)
m.addConstr(6*x1 + 4*x5 + 7*x7 >= 22)
m.addConstr(6*x1 + 9*x2 + 15*x6 >= 22)
m.addConstr(9*x3 + 10*x4 + 15*x6 >= 13)
m.addConstr(9*x3 + 4*x5 + 7*x7 >= 13)
m.addConstr(6*x1 + 4*x5 + 7*x7 >= 13)
m.addConstr(6*x1 + 9*x2 + 15*x6 >= 13)
m.addConstr(9*x3 + 10*x4 + 15*x6 >= 16)
m.addConstr(9*x3 + 4*x5 + 7*x7 >= 16)
m.addConstr(6*x1 + 4*x5 + 7*x7 >= 16)
m.addConstr(6*x1 + 9*x2 + 15*x6 >= 16)
m.addConstr(-4*x4 + 10*x7 >= 0)
m.addConstr(6*x1 + 4*x5 <= 40)
m.addConstr(9*x2 + 10*x4 <= 136)
m.addConstr(4*x5 + 15*x6 <= 34)
m.addConstr(6*x1 + 10*x4 <= 52)
m.addConstr(9*x3 + 7*x7 <= 141)
m.addConstr(15*x6 + 7*x7 <= 108)
m.addConstr(9*x3 + 4*x5 <= 104)
m.addConstr(9*x2 + 9*x3 <= 53)
m.addConstr(9*x3 + 15*x6 <= 64)
m.addConstr(9*x2 + 15*x6 <= 158)
m.addConstr(4*x5 + 7*x7 <= 61)
m.addConstr(10*x4 + 15*x6 <= 35)
m.addConstr(6*x1 + 15*x6 <= 116)
m.addConstr(6*x1 + 4*x5 + 15*x6 <= 120)
m.addConstr(6*x1 + 9*x2 + 9*x3 + 10*x4 + 4*x5 + 15*x6 + 7*x7 <= 120)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("lanyards: ", x1.varValue)
    print("mechanical_pencils: ", x2.varValue)
    print("red_pens: ", x3.varValue)
    print("blue_pens: ", x4.varValue)
    print("monochrome_printers: ", x5.varValue)
    print("packs_of_paper: ", x6.varValue)
    print("black_pens: ", x7.varValue)
else:
    print("The model is infeasible")
```