To tackle this problem, we first need to translate the given natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the provided information.

### Symbolic Representation

Let's denote:
- $x_0$ as the quantity of wooden pencils,
- $x_1$ as the quantity of 3D printers.

The objective function described is to maximize: $7(x_0 \cdot x_1) + 7(x_0) + 7(x_1)$.

Constraints based on the description:
1. Employee satisfaction impact from wooden pencils and 3D printers should be at least 15: $8x_0 + 16x_1 \geq 15$.
2. The total combined workplace safety impact from wooden pencils squared and 3D printers squared has to be 17 or more: $(17x_0)^2 + (5x_1)^2 \geq 17$.
3. Total combined usefulness rating should be at minimum 45: $2x_0 + 12x_1 \geq 45$.
4. At least 22 sq. ft of storage space must be used: $2x_0 + 8x_1 \geq 22$.
5. $-1(x_0)^2 + 9(x_1)^2 \geq 0$.
6. Total combined employee satisfaction impact should not exceed 35: $8x_0 + 16x_1 \leq 35$.
7. The total combined workplace safety impact from wooden pencils and 3D printers should be no more than 54: $(17x_0) + (5x_1) \leq 54$.
8. Total combined usefulness rating squared has to be 103 at maximum: $(2x_0)^2 + (12x_1)^2 \leq 103$.
9. A maximum of 51 sq. ft of storage space can be used for wooden pencils and 3D printers: $2x_0 + 8x_1 \leq 51$.

### Symbolic Representation in JSON Format
```json
{
    'sym_variables': [('x0', 'wooden pencils'), ('x1', '3D printers')],
    'objective_function': '7*(x0*x1) + 7*x0 + 7*x1',
    'constraints': [
        '8*x0 + 16*x1 >= 15',
        '(17*x0)**2 + (5*x1)**2 >= 17',
        '2*x0 + 12*x1 >= 45',
        '2*x0 + 8*x1 >= 22',
        '-(x0**2) + 9*(x1**2) >= 0',
        '8*x0 + 16*x1 <= 35',
        '(17*x0) + (5*x1) <= 54',
        '(2*x0)**2 + (12*x1)**2 <= 103',
        '2*x0 + 8*x1 <= 51'
    ]
}
```

### Gurobi Code
```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="wooden_pencils")
x1 = m.addVar(vtype=GRB.INTEGER, name="3D_printers")

# Objective function
m.setObjective(7*(x0*x1) + 7*x0 + 7*x1, GRB.MAXIMIZE)

# Constraints
m.addConstr(8*x0 + 16*x1 >= 15, "employee_satisfaction_min")
m.addConstr((17*x0)**2 + (5*x1)**2 >= 17, "workplace_safety_squared_min")
m.addConstr(2*x0 + 12*x1 >= 45, "usefulness_rating_min")
m.addConstr(2*x0 + 8*x1 >= 22, "storage_space_min")
m.addConstr(-(x0**2) + 9*(x1**2) >= 0, "non_negative_constraint")
m.addConstr(8*x0 + 16*x1 <= 35, "employee_satisfaction_max")
m.addConstr((17*x0) + (5*x1) <= 54, "workplace_safety_max")
m.addConstr((2*x0)**2 + (12*x1)**2 <= 103, "usefulness_rating_squared_max")
m.addConstr(2*x0 + 8*x1 <= 51, "storage_space_max")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Wooden Pencils: {x0.x}")
    print(f"3D Printers: {x1.x}")
else:
    print("No optimal solution found")
```