## Step 1: Define the symbolic representation of the variables
The variables are 'wooden pencils' and '3D printers', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $7x_1x_2 + 7x_1 + 7x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $8x_1 + 16x_2 \geq 15$ (employee satisfaction impact minimum)
- $17^2x_1^2 + 5^2x_2^2 \geq 17$ (workplace safety impact squared minimum)
- $2x_1 + 12x_2 \geq 45$ (usefulness rating minimum)
- $2x_1 + 8x_2 \geq 22$ (storage space minimum)
- $-x_1^2 + 9x_2^2 \geq 0$ (mixed constraint)
- $8x_1 + 16x_2 \leq 35$ (employee satisfaction impact maximum)
- $17x_1 + 5x_2 \leq 54$ (workplace safety impact maximum)
- $2^2x_1^2 + 12^2x_2^2 \leq 103$ (usefulness rating squared maximum)
- $2x_1 + 8x_2 \leq 51$ (storage space maximum)

## Step 4: Correct and Simplify Constraints for Accuracy
Correcting and simplifying the constraints for accuracy:
- The employee satisfaction impact constraints are $8x_1 + 16x_2 \geq 15$ and $8x_1 + 16x_2 \leq 35$.
- The workplace safety impact constraints are $17x_1 + 5x_2 \leq 54$ and $(17x_1)^2 + (5x_2)^2 \geq 17$.
- Other constraints remain as listed.

## 5: Write the Gurobi Code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="wooden_pencils", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="3D_printers", vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(7 * x1 * x2 + 7 * x1 + 7 * x2, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(8 * x1 + 16 * x2 >= 15, name="employee_satisfaction_min")
model.addConstr(17 * x1 + 5 * x2 <= 54, name="workplace_safety_max")
model.addConstr(2 * x1 + 12 * x2 >= 45, name="usefulness_rating_min")
model.addConstr(2 * x1 + 8 * x2 >= 22, name="storage_space_min")
model.addConstr(-x1**2 + 9 * x2**2 >= 0, name="mixed_constraint")
model.addConstr(8 * x1 + 16 * x2 <= 35, name="employee_satisfaction_max")
model.addConstr((17 * x1)**2 + (5 * x2)**2 >= 17, name="workplace_safety_squared_min")
model.addConstr(2**2 * x1**2 + 12**2 * x2**2 <= 103, name="usefulness_rating_squared_max")
model.addConstr(2 * x1 + 8 * x2 <= 51, name="storage_space_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Wooden Pencils: ", x1.varValue)
    print("3D Printers: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 6: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'wooden pencils'), ('x2', '3D printers')],
    'objective_function': '7*x1*x2 + 7*x1 + 7*x2',
    'constraints': [
        '8*x1 + 16*x2 >= 15',
        '17*x1 + 5*x2 <= 54',
        '2*x1 + 12*x2 >= 45',
        '2*x1 + 8*x2 >= 22',
        '-x1^2 + 9*x2^2 >= 0',
        '8*x1 + 16*x2 <= 35',
        '(17*x1)^2 + (5*x2)^2 >= 17',
        '2^2*x1^2 + 12^2*x2^2 <= 103',
        '2*x1 + 8*x2 <= 51'
    ]
}
```