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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $3x_1^2 + 7x_1x_2 + 7x_2^2 + 4x_1$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $5x_1 = 5$ (Laura's work quality rating is 5, but this seems to be a misunderstanding since the rating is given as a constant and not a coefficient of $x_1$. Assuming it means $x_0 = 5$ for Laura, but $x_0$ is not a variable we are optimizing over, it's a given attribute. So we consider $5x_1$ as part of the work quality calculation, not a direct constraint on $x_1$),
2. $2x_2$ (Bobby's work quality rating),
3. $5x_1 + 2x_2 \geq 25$ (total combined work quality rating),
4. $8x_1 - 10x_2 \geq 0$,
5. $5^2x_1^2 + 2^2x_2^2 \leq 58$ or more accurately based on given data: $x_0^2 + x_1^2 \leq 58$ translates to $5^2 + 2^2 \leq 58$ when considering $x_0, x_1$ as given, but actually, we have $x_1^2 + x_2^2 \leq 58 / (73/25)$ which seems incorrect based on direct translation. Correctly it is $5x_1 + 2x_2 \geq 25$ and $x_1^2 + x_2^2 \leq 58$ seems not directly derived from given data.

## 4: Correctly interpret given data for constraints
Given attributes: 
- 'r0': {'description': 'work quality rating', 'upper_bound': 73, 'x0': 5, 'x1': 2}
This implies that work quality ratings are associated with Laura and Bobby but are constants.

## 5: Formulate the optimization problem
Let's assume $x_1$ is 'hours worked by Laura' and $x_2$ is 'hours worked by Bobby'.

## 6: Write down the optimization problem
Minimize $3x_1^2 + 7x_1x_2 + 7x_2^2 + 4x_1$

Subject to:
- $5x_1 + 2x_2 \geq 25$
- $8x_1 - 10x_2 \geq 0$
- $x_1^2 + x_2^2 \leq 58$

## 7: Symbolic representation
```json
{
'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Bobby')],
'objective_function': '3*x1^2 + 7*x1*x2 + 7*x2^2 + 4*x1',
'constraints': [
    '5*x1 + 2*x2 >= 25',
    '8*x1 - 10*x2 >= 0',
    'x1^2 + x2^2 <= 58'
]
}
```

## 8: Gurobi code
```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
x1 = m.addVar(name="hours_worked_by_Laura", lb=0)  # Laura
x2 = m.addVar(name="hours_worked_by_Bobby", lb=0)  # Bobby

# Objective function
m.setObjective(3*x1**2 + 7*x1*x2 + 7*x2**2 + 4*x1, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(5*x1 + 2*x2 >= 25, name="work_quality_rating")
m.addConstr(8*x1 - 10*x2 >= 0, name="work_hours_constraint")
m.addConstr(x1**2 + x2**2 <= 58, name="work_quality_rating_squared")

# Solve the model
m.optimize()

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