## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'wooden pencils', 'smoke detectors', and 'mechanical pencils', which we can 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 $1.14x_0 + 7.94x_1 + 2.93x_2$.

## Step 3: List all constraints in symbolic notation
1. $x_0 \geq 0$ and $x_0$ is an integer (nonfractional number of wooden pencils)
2. $x_1 \geq 0$ and $x_1$ is an integer (The amount of smoke detectors must be a whole number)
3. $x_2 \geq 0$ and $x_2$ is an integer (The number of mechanical pencils must be a whole number)
4. $x_0 + 7x_1 \geq 15$ (You can spend no less than $15 on smoke detectors, and mechanical pencils)
5. $x_0 + 7x_1 + 10x_2 \geq 21$ (You must spend at least $21 on wooden pencils plus smoke detectors plus mechanical pencils)
6. $8x_0 + 3x_1 + 5x_2 \geq 18$ (The total combined employee satisfaction impact from wooden pencils plus smoke detectors plus mechanical pencils should be 18 at a minimum)
7. $7x_0 + 3x_1 \geq 11$ (The total combined workplace safety impact from wooden pencils, and smoke detectors should be no less than 11)
8. $3x_1 + 9x_2 \geq 24$ (The total combined workplace safety impact from smoke detectors, and mechanical pencils must be 24 at a minimum)
9. $7x_0 + 9x_2 \geq 14$ (The total combined workplace safety impact from wooden pencils plus mechanical pencils must be at least 14)
10. $7x_0 + 3x_1 + 9x_2 \geq 14$ (The total combined workplace safety impact from wooden pencils, smoke detectors, and mechanical pencils has to be equal to or greater than 14)
11. $x_1 + 11x_2 \geq 36$ (smoke detectors plus mechanical pencils must occupy at least 36 ft^2 of storage space)
12. $7x_0 + x_1 \geq 23$ (You must use at least 23 sq. ft of storage space on wooden pencils, and smoke detectors)
13. $7x_0 + x_1 + 11x_2 \geq 23$ (You must use at least 23 ft^2 of storage space on wooden pencils plus smoke detectors plus mechanical pencils)
14. $-5x_0 + 3x_2 \geq 0$ (minus five times the number of wooden pencils, plus three times the number of mechanical pencils should be at least zero)
15. $-7x_1 + 10x_2 \geq 0$ ( -7 times the number of smoke detectors, plus 10 times the number of mechanical pencils should be greater than or equal to zero)
16. $x_0 + 7x_1 \leq 61$ (wooden pencils plus smoke detectors must cost a total of at most 61 dollars)
17. $x_0 + 10x_2 \leq 66$ (wooden pencils, and mechanical pencils must cost a total of at most $66)
18. $3x_1 + 5x_2 \leq 29$ (The total combined employee satisfaction impact from smoke detectors, and mechanical pencils should be 29 or less)
19. $8x_0 + 5x_2 \leq 55$ (The total combined employee satisfaction impact from wooden pencils and mechanical pencils should be 55 at a maximum)
20. $7x_0 + 11x_2 \leq 87$ (Up to 87 square feet of storage space can be used for wooden pencils plus mechanical pencils)
21. $x_1 + 11x_2 \leq 47$ (You're not allowed to use more than 47 sq. ft of storage space for smoke detectors plus mechanical pencils)
22. $7x_0 + x_1 + 11x_2 \leq 96$ (wooden pencils plus smoke detectors plus mechanical pencils must take up no more than 96 square feet of storage space)

## 4: Define the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ['x0', 'wooden pencils'],
        ['x1', 'smoke detectors'],
        ['x2', 'mechanical pencils']
    ],
    'objective_function': '1.14x0 + 7.94x1 + 2.93x2',
    'constraints': [
        'x0 >= 0',
        'x1 >= 0',
        'x2 >= 0',
        'x0 + 7x1 >= 15',
        'x0 + 7x1 + 10x2 >= 21',
        '8x0 + 3x1 + 5x2 >= 18',
        '7x0 + 3x1 >= 11',
        '3x1 + 9x2 >= 24',
        '7x0 + 9x2 >= 14',
        '7x0 + 3x1 + 9x2 >= 14',
        'x1 + 11x2 >= 36',
        '7x0 + x1 >= 23',
        '7x0 + x1 + 11x2 >= 23',
        '-5x0 + 3x2 >= 0',
        '-7x1 + 10x2 >= 0',
        'x0 + 7x1 <= 61',
        'x0 + 10x2 <= 66',
        '3x1 + 5x2 <= 29',
        '8x0 + 5x2 <= 55',
        '7x0 + 11x2 <= 87',
        'x1 + 11x2 <= 47',
        '7x0 + x1 + 11x2 <= 96',
        'x0 % 1 == 0',
        'x1 % 1 == 0',
        'x2 % 1 == 0'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name='wooden_pencils', vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name='smoke_detectors', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='mechanical_pencils', vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(1.14 * x0 + 7.94 * x1 + 2.93 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(x0 >= 0)
m.addConstr(x1 >= 0)
m.addConstr(x2 >= 0)
m.addConstr(x0 + 7 * x1 >= 15)
m.addConstr(x0 + 7 * x1 + 10 * x2 >= 21)
m.addConstr(8 * x0 + 3 * x1 + 5 * x2 >= 18)
m.addConstr(7 * x0 + 3 * x1 >= 11)
m.addConstr(3 * x1 + 9 * x2 >= 24)
m.addConstr(7 * x0 + 9 * x2 >= 14)
m.addConstr(7 * x0 + 3 * x1 + 9 * x2 >= 14)
m.addConstr(x1 + 11 * x2 >= 36)
m.addConstr(7 * x0 + x1 >= 23)
m.addConstr(7 * x0 + x1 + 11 * x2 >= 23)
m.addConstr(-5 * x0 + 3 * x2 >= 0)
m.addConstr(-7 * x1 + 10 * x2 >= 0)
m.addConstr(x0 + 7 * x1 <= 61)
m.addConstr(x0 + 10 * x2 <= 66)
m.addConstr(3 * x1 + 5 * x2 <= 29)
m.addConstr(8 * x0 + 5 * x2 <= 55)
m.addConstr(7 * x0 + 11 * x2 <= 87)
m.addConstr(x1 + 11 * x2 <= 47)
m.addConstr(7 * x0 + x1 + 11 * x2 <= 96)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objval)
    print('Wooden Pencils: ', x0.varValue)
    print('Smoke Detectors: ', x1.varValue)
    print('Mechanical Pencils: ', x2.varValue)
else:
    print('No solution found')
```