## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Jean' and 'hours worked by Laura', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $1x_1^2 + 7x_1x_2 + 1x_2^2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $21x_1 + 24x_2 \geq 46$ (paperwork competence rating)
- $1x_1 + 16x_2 \geq 39$ (dollar cost per hour)
- $21x_1 + 28x_2 \geq 22$ (work quality rating)
- $8x_1^2 - 9x_2^2 \geq 0$ (non-linear constraint)
- $21^2x_1^2 + 24^2x_2^2 \leq 90$ (paperwork competence rating squared)
- $1x_1 + 16x_2 \leq 80$ (dollar cost per hour upper bound)
- $21x_1 + 28x_2 \leq 70$ (work quality rating upper bound)

## 4: Correct and simplify constraints for accuracy
Correcting and simplifying:
- The paperwork competence rating constraint is $21x_1 + 24x_2 \geq 46$.
- The dollar cost per hour constraint is $1x_1 + 16x_2 \geq 39$.
- The work quality rating constraint is $21x_1 + 28x_2 \geq 22$.
- The non-linear constraint is $8x_1^2 - 9x_2^2 \geq 0$.
- The squared paperwork competence rating constraint is $(21x_1)^2 + (24x_2)^2 \leq 90$ which simplifies to $441x_1^2 + 576x_2^2 \leq 90$.
- The dollar cost per hour upper bound is $1x_1 + 16x_2 \leq 80$.
- The work quality rating upper bound is $21x_1 + 28x_2 \leq 70$.

## 5: Create the symbolic representation dictionary
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'hours worked by Jean'), ('x2', 'hours worked by Laura')],
    'objective_function': '1*x1^2 + 7*x1*x2 + 1*x2^2',
    'constraints': [
        '21*x1 + 24*x2 >= 46',
        '1*x1 + 16*x2 >= 39',
        '21*x1 + 28*x2 >= 22',
        '8*x1^2 - 9*x2^2 >= 0',
        '441*x1^2 + 576*x2^2 <= 90',
        '1*x1 + 16*x2 <= 80',
        '21*x1 + 28*x2 <= 70'
    ]
}
```

## 6: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="hours_worked_by_Jean")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="hours_worked_by_Laura")

    # Define the objective function
    model.setObjective(1*x1**2 + 7*x1*x2 + 1*x2**2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(21*x1 + 24*x2 >= 46, name="paperwork_competence_rating")
    model.addConstr(1*x1 + 16*x2 >= 39, name="dollar_cost_per_hour")
    model.addConstr(21*x1 + 28*x2 >= 22, name="work_quality_rating")
    model.addConstr(8*x1**2 - 9*x2**2 >= 0, name="non_linear_constraint")
    model.addConstr(441*x1**2 + 576*x2**2 <= 90, name="paperwork_competence_rating_squared")
    model.addConstr(1*x1 + 16*x2 <= 80, name="dollar_cost_per_hour_upper_bound")
    model.addConstr(21*x1 + 28*x2 <= 70, name="work_quality_rating_upper_bound")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Jean: {x1.varValue}")
        print(f"Hours worked by Laura: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```