## Step 1: Define the symbolic representation of the variables
The variables are: ['staplers', 'headsets', 'planners', 'blue pens', 'office chairs', 'smoke detectors']. 
We can represent them symbolically as: [('x0', 'staplers'), ('x1', 'headsets'), ('x2', 'planners'), ('x3', 'blue pens'), ('x4', 'office chairs'), ('x5', 'smoke detectors')].

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is: $7.67 \times staplers + 1.84 \times headsets + 4.52 \times planners + 8.41 \times blue\ pens + 6.13 \times office\ chairs + 4.21 \times smoke\ detectors$.
In symbolic notation, this is: $7.67x_0 + 1.84x_1 + 4.52x_2 + 8.41x_3 + 6.13x_4 + 4.21x_5$.

## 3: List the constraints in symbolic notation
1. $14x_1 + 12x_3 \geq 24$
2. $x_0 + 12x_3 \geq 18$
3. $14x_1 + 8x_2 + 7x_4 \geq 23$
4. $4x_1 + x_2 \geq 14$
5. $x_2 + 4x_3 \geq 35$
6. $x_0 + x_2 \geq 26$
7. $4x_3 + 10x_4 \geq 33$
8. $x_2 + 10x_4 \geq 36$
9. $4x_1 + 13x_5 \geq 42$
10. $10x_4 + 13x_5 \geq 25$
11. $x_0 + 10x_4 \geq 21$
12. $x_0 + 8x_2 \leq 104$
13. $x_0 + 7x_5 \leq 84$
14. $8x_2 + 12x_3 \leq 150$
15. $7x_4 + 7x_5 \leq 188$
16. $12x_3 + 7x_4 \leq 81$
17. $x_0 + 14x_1 \leq 122$
18. $14x_1 + 8x_2 \leq 137$
19. $x_0 + 7x_4 \leq 105$
20. $14x_1 + 12x_3 \leq 92$
21. $x_0 + x_1 + x_2 + x_3 + x_4 + x_5 \leq 92$
22. $x_2 + 13x_5 \leq 117$
23. $x_2 + 10x_4 \leq 206$
24. $x_0 + 13x_5 \leq 61$
25. $4x_3 + 13x_5 \leq 115$
26. $10x_4 + 13x_5 \leq 136$
27. $x_0 + 4x_1 \leq 222$
28. $x_2 + 4x_3 \leq 145$
29. $4x_1 + 13x_5 \leq 159$
30. $x_0 + x_2 \leq 51$
31. $x_0 + x_1 + x_2 + x_3 + x_4 + x_5 \leq 51$

## 4: Convert the problem into Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="staplers", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="headsets", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="planners", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="blue_pens", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="office_chairs", vtype=gurobi.GRB.INTEGER)
x5 = m.addVar(name="smoke_detectors", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(7.67 * x0 + 1.84 * x1 + 4.52 * x2 + 8.41 * x3 + 6.13 * x4 + 4.21 * x5, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(14 * x1 + 12 * x3 >= 24)
m.addConstr(x0 + 12 * x3 >= 18)
m.addConstr(14 * x1 + 8 * x2 + 7 * x4 >= 23)
m.addConstr(4 * x1 + x2 >= 14)
m.addConstr(x2 + 4 * x3 >= 35)
m.addConstr(x0 + x2 >= 26)
m.addConstr(4 * x3 + 10 * x4 >= 33)
m.addConstr(x2 + 10 * x4 >= 36)
m.addConstr(4 * x1 + 13 * x5 >= 42)
m.addConstr(10 * x4 + 13 * x5 >= 25)
m.addConstr(x0 + 10 * x4 >= 21)
m.addConstr(x0 + 8 * x2 <= 104)
m.addConstr(x0 + 7 * x5 <= 84)
m.addConstr(8 * x2 + 12 * x3 <= 150)
m.addConstr(7 * x4 + 7 * x5 <= 188)
m.addConstr(12 * x3 + 7 * x4 <= 81)
m.addConstr(x0 + 14 * x1 <= 122)
m.addConstr(14 * x1 + 8 * x2 <= 137)
m.addConstr(x0 + 7 * x4 <= 105)
m.addConstr(14 * x1 + 12 * x3 <= 92)
m.addConstr(x0 + x1 + x2 + x3 + x4 + x5 <= 92)
m.addConstr(x2 + 13 * x5 <= 117)
m.addConstr(x2 + 10 * x4 <= 206)
m.addConstr(x0 + 13 * x5 <= 61)
m.addConstr(4 * x3 + 13 * x5 <= 115)
m.addConstr(10 * x4 + 13 * x5 <= 136)
m.addConstr(x0 + 4 * x1 <= 222)
m.addConstr(x2 + 4 * x3 <= 145)
m.addConstr(4 * x1 + 13 * x5 <= 159)
m.addConstr(x0 + x2 <= 51)
m.addConstr(x0 + x1 + x2 + x3 + x4 + x5 <= 51)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Staplers: ", x0.varValue)
    print("Headsets: ", x1.varValue)
    print("Planners: ", x2.varValue)
    print("Blue Pens: ", x3.varValue)
    print("Office Chairs: ", x4.varValue)
    print("Smoke Detectors: ", x5.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic representation of the problem
```json
{
    "sym_variables": [
        ("x0", "staplers"),
        ("x1", "headsets"),
        ("x2", "planners"),
        ("x3", "blue pens"),
        ("x4", "office chairs"),
        ("x5", "smoke detectors")
    ],
    "objective_function": "7.67x0 + 1.84x1 + 4.52x2 + 8.41x3 + 6.13x4 + 4.21x5",
    "constraints": [
        "14x1 + 12x3 >= 24",
        "x0 + 12x3 >= 18",
        "14x1 + 8x2 + 7x4 >= 23",
        "4x1 + x2 >= 14",
        "x2 + 4x3 >= 35",
        "x0 + x2 >= 26",
        "4x3 + 10x4 >= 33",
        "x2 + 10x4 >= 36",
        "4x1 + 13x5 >= 42",
        "10x4 + 13x5 >= 25",
        "x0 + 10x4 >= 21",
        "x0 + 8x2 <= 104",
        "x0 + 7x5 <= 84",
        "8x2 + 12x3 <= 150",
        "7x4 + 7x5 <= 188",
        "12x3 + 7x4 <= 81",
        "x0 + 14x1 <= 122",
        "14x1 + 8x2 <= 137",
        "x0 + 7x4 <= 105",
        "14x1 + 12x3 <= 92",
        "x0 + x1 + x2 + x3 + x4 + x5 <= 92",
        "x2 + 13x5 <= 117",
        "x2 + 10x4 <= 206",
        "x0 + 13x5 <= 61",
        "4x3 + 13x5 <= 115",
        "10x4 + 13x5 <= 136",
        "x0 + 4x1 <= 222",
        "x2 + 4x3 <= 145",
        "4x1 + 13x5 <= 159",
        "x0 + x2 <= 51",
        "x0 + x1 + x2 + x3 + x4 + x5 <= 51"
    ]
}
```