## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George', 'hours worked by Bill', and 'hours worked by Laura', which can be represented as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $8x_0^2 + 8x_0x_1 + 8x_0x_2 + 9x_1^2 + 6x_1x_2 + x_2^2 + 3x_0 + 4x_1 + 5x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $26x_0 \leq 200$ (likelihood to quit index for George)
- $5x_0 \leq 138$ (productivity rating for George)
- $20x_0 \leq 233$ (organization score for George)
- $1x_0 \leq 219$ (work quality rating for George)
- $3x_0 \leq 198$ (dollar cost per hour for George)
- $3x_1 \leq 200$ (likelihood to quit index for Bill)
- $15x_1 \leq 138$ (productivity rating for Bill)
- $24x_1 \leq 233$ (organization score for Bill)
- $23x_1 \leq 219$ (work quality rating for Bill)
- $12x_1 \leq 198$ (dollar cost per hour for Bill)
- $22x_2 \leq 200$ (likelihood to quit index for Laura)
- $12x_2 \leq 138$ (productivity rating for Laura)
- $19x_2 \leq 233$ (organization score for Laura)
- $29x_2 \leq 219$ (work quality rating for Laura)
- $3x_2 \leq 198$ (dollar cost per hour for Laura)
- $3x_1^2 + 22x_2^2 \geq 64$ (combined likelihood to quit index)
- $26x_0 + 3x_1 + 22x_2 \geq 64$ (combined likelihood to quit index)
- $15x_1 + 12x_2 \geq 16$ (combined productivity rating)
- $5x_0^2 + 12x_2^2 \geq 37$ (combined productivity rating)
- $5x_0 + 15x_1 + 12x_2 \geq 37$ (combined productivity rating)
- $20x_0^2 + 19x_2^2 \geq 77$ (combined organization score)
- $20x_0 + 24x_1 \geq 74$ (combined organization score)
- $20x_0 + 24x_1 + 19x_2 \geq 74$ (combined organization score)
- $1x_0 + 23x_1 \geq 29$ (combined work quality rating)
- $23x_1 + 29x_2 \geq 61$ (combined work quality rating)
- $1x_0^2 + 23x_1^2 + 29x_2^2 \geq 72$ (combined work quality rating)
- $1x_0 + 23x_1 + 29x_2 \geq 72$ (combined work quality rating)
- $3x_0 + 3x_2 \geq 58$ (combined dollar cost per hour)
- $12x_1 + 3x_2 \geq 54$ (combined dollar cost per hour)
- $3x_0 + 12x_1 + 3x_2 \geq 54$ (combined dollar cost per hour)
- $10x_0^2 - 8x_2^2 \geq 0$ (additional constraint)
- $9x_0 - 4x_1 \geq 0$ (additional constraint)
- $26x_0 + 3x_1 \leq 111$ (additional constraint)
- $5x_0 + 12x_2 \leq 115$ (additional constraint)
- $12x_1 + 3x_2 \leq 111$ (additional constraint)
- $x_0$ is an integer
- $x_1$ is a float
- $x_2$ is a float

## Step 4: Convert the problem into Gurobi code
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="x0", vtype=gp.GRB.INTEGER)  # hours worked by George
x1 = m.addVar(name="x1")  # hours worked by Bill
x2 = m.addVar(name="x2")  # hours worked by Laura

# Define the objective function
m.setObjective(8*x0**2 + 8*x0*x1 + 8*x0*x2 + 9*x1**2 + 6*x1*x2 + x2**2 + 3*x0 + 4*x1 + 5*x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(26*x0 <= 200)
m.addConstr(5*x0 <= 138)
m.addConstr(20*x0 <= 233)
m.addConstr(x0 <= 219)
m.addConstr(3*x0 <= 198)

m.addConstr(3*x1 <= 200)
m.addConstr(15*x1 <= 138)
m.addConstr(24*x1 <= 233)
m.addConstr(23*x1 <= 219)
m.addConstr(12*x1 <= 198)

m.addConstr(22*x2 <= 200)
m.addConstr(12*x2 <= 138)
m.addConstr(19*x2 <= 233)
m.addConstr(29*x2 <= 219)
m.addConstr(3*x2 <= 198)

m.addConstr(3*x1**2 + 22*x2**2 >= 64)
m.addConstr(26*x0 + 3*x1 + 22*x2 >= 64)
m.addConstr(15*x1 + 12*x2 >= 16)
m.addConstr(5*x0**2 + 12*x2**2 >= 37)
m.addConstr(5*x0 + 15*x1 + 12*x2 >= 37)
m.addConstr(20*x0**2 + 19*x2**2 >= 77)
m.addConstr(20*x0 + 24*x1 >= 74)
m.addConstr(20*x0 + 24*x1 + 19*x2 >= 74)
m.addConstr(x0 + 23*x1 >= 29)
m.addConstr(23*x1 + 29*x2 >= 61)
m.addConstr(x0**2 + 23*x1**2 + 29*x2**2 >= 72)
m.addConstr(x0 + 23*x1 + 29*x2 >= 72)
m.addConstr(3*x0 + 3*x2 >= 58)
m.addConstr(12*x1 + 3*x2 >= 54)
m.addConstr(3*x0 + 12*x1 + 3*x2 >= 54)
m.addConstr(10*x0**2 - 8*x2**2 >= 0)
m.addConstr(9*x0 - 4*x1 >= 0)
m.addConstr(26*x0 + 3*x1 <= 111)
m.addConstr(5*x0 + 12*x2 <= 115)
m.addConstr(12*x1 + 3*x2 <= 111)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by George'), ('x1', 'hours worked by Bill'), ('x2', 'hours worked by Laura')],
    'objective_function': '8*x0^2 + 8*x0*x1 + 8*x0*x2 + 9*x1^2 + 6*x1*x2 + x2^2 + 3*x0 + 4*x1 + 5*x2',
    'constraints': [
        '26*x0 <= 200',
        '5*x0 <= 138',
        '20*x0 <= 233',
        'x0 <= 219',
        '3*x0 <= 198',
        '3*x1 <= 200',
        '15*x1 <= 138',
        '24*x1 <= 233',
        '23*x1 <= 219',
        '12*x1 <= 198',
        '22*x2 <= 200',
        '12*x2 <= 138',
        '19*x2 <= 233',
        '29*x2 <= 219',
        '3*x2 <= 198',
        '3*x1^2 + 22*x2^2 >= 64',
        '26*x0 + 3*x1 + 22*x2 >= 64',
        '15*x1 + 12*x2 >= 16',
        '5*x0^2 + 12*x2^2 >= 37',
        '5*x0 + 15*x1 + 12*x2 >= 37',
        '20*x0^2 + 19*x2^2 >= 77',
        '20*x0 + 24*x1 >= 74',
        '20*x0 + 24*x1 + 19*x2 >= 74',
        'x0 + 23*x1 >= 29',
        '23*x1 + 29*x2 >= 61',
        'x0^2 + 23*x1^2 + 29*x2^2 >= 72',
        'x0 + 23*x1 + 29*x2 >= 72',
        '3*x0 + 3*x2 >= 58',
        '12*x1 + 3*x2 >= 54',
        '3*x0 + 12*x1 + 3*x2 >= 54',
        '10*x0^2 - 8*x2^2 >= 0',
        '9*x0 - 4*x1 >= 0',
        '26*x0 + 3*x1 <= 111',
        '5*x0 + 12*x2 <= 115',
        '12*x1 + 3*x2 <= 111'
    ]
}
```