## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bill', 'hours worked by Mary', 'hours worked by George', 'hours worked by Dale']. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $5x_0^2 + 5x_0x_1 + x_0x_2 + 4x_0x_3 + 8x_1^2 + x_1x_3 + 4x_2^2 + x_2x_3 + 6x_3^2 + x_1 + x_2 + 7x_3$.

## Step 3: List the constraints
The constraints are:
- $15x_0 \leq 212$
- $x_0 \leq 15$ (from organization score)
- $x_0 \geq 0$ is implicit
- $1x_0 \leq 304$ (from productivity rating, but seems to be an upper bound for individual ratings, not directly used)
- $7x_0 \leq 320$ (from paperwork competence rating)
- $13x_0 \leq 153$ (from computer competence rating)

- $5x_1 \leq 212$
- $13x_1 \leq 304$
- $12x_1 \leq 320$
- $x_1 \leq 1$

- $4x_2 \leq 212$
- $14x_2 \leq 304$
- $13x_2 \leq 320$
- $17x_2 \leq 153$

- $9x_3 \leq 212$
- $10x_3 \leq 304$
- $11x_3 \leq 320$
- $12x_3 \leq 153$

- $15x_0 + 4x_2 \geq 47$
- $15x_0^2 + 9x_3^2 \geq 30$
- $5x_1 + 4x_2 \geq 19$
- $15x_0 + 5x_1 \geq 50$
- $15x_0 + 4x_2 + 9x_3 \geq 38$
- $5x_1 + 4x_2 + 9x_3 \geq 38$
- $15x_0 + 4x_2 + 9x_3 \geq 49$
- $5x_1 + 4x_2 + 9x_3 \geq 49$

- $1x_0 + 10x_3 \geq 29$
- $7x_0 + 12x_1 \geq 59$
- $12x_1 + 13x_2 \geq 35$
- $7x_0^2 + 13x_2^2 \geq 41$
- $13x_2^2 + 11x_3^2 \geq 31$
- $7x_0^2 + 12x_1^2 + 11x_3^2 \geq 40$

- $4x_2 + 9x_3 \leq 121$
- $5x_1 + 9x_3 \leq 142$
- $15x_0^2 + 4x_2^2 \leq 80$
- $15x_0 + 5x_1 + 9x_3 \leq 63$
- $15x_0 + 5x_1 + 4x_2 + 9x_3 \leq 63$

- $1x_0^2 + 14x_2^2 \leq 164$
- $1x_0 + 10x_3 \leq 252$
- $1x_0 + 14x_2 + 10x_3 \leq 261$
- $1x_0 + 13x_1 + 14x_2 \leq 232$
- $1x_0 + 13x_1 + 14x_2 + 10x_3 \leq 232$

- $12x_1 + 11x_3 \leq 158$
- $7x_0 + 13x_2 \leq 84$
- $13x_2 + 11x_3 \leq 215$
- $7x_0 + 11x_3 \leq 296$
- $7x_0 + 12x_1 \leq 220$

- $12x_1^2 + 13x_2^2 \leq 162$
- $7x_0 + 12x_1 + 13x_2 + 11x_3 \leq 162$

- $13x_0^2 + x_1^2 \leq 70$
- $17x_2 + 12x_3 \leq 62$
- $13x_0^2 + x_1^2 + 17x_2^2 \leq 80$
- $17x_2 + 12x_3 + x_1 \leq 48$
- $13x_0 + x_1 + 17x_2 + 12x_3 \leq 48$

## Step 4: Write down the Gurobi code
```python
import gurobi

# Define variables
m = gurobi.Model()
x0 = m.addVar(lb=-gurobi.GRB.INFINITY, name='x0')  # hours worked by Bill
x1 = m.addVar(lb=-gurobi.GRB.INFINITY, name='x1')  # hours worked by Mary
x2 = m.addVar(lb=-gurobi.GRB.INFINITY, name='x2')  # hours worked by George
x3 = m.addVar(lb=-gurobi.GRB.INFINITY, name='x3')  # hours worked by Dale

# Objective function
m.setObjective(5*x0**2 + 5*x0*x1 + x0*x2 + 4*x0*x3 + 8*x1**2 + x1*x3 + 4*x2**2 + x2*x3 + 6*x3**2 + x1 + x2 + 7*x3, gurobi.GRB.MAXIMIZE)

# Constraints
# Individual constraints
m.addConstr(15*x0 <= 212)
m.addConstr(x0 >= 0)
m.addConstr(1*x0 <= 304)
m.addConstr(7*x0 <= 320)
m.addConstr(13*x0 <= 153)

m.addConstr(5*x1 <= 212)
m.addConstr(13*x1 <= 304)
m.addConstr(12*x1 <= 320)
m.addConstr(x1 >= 0)

m.addConstr(4*x2 <= 212)
m.addConstr(14*x2 <= 304)
m.addConstr(13*x2 <= 320)
m.addConstr(17*x2 <= 153)

m.addConstr(9*x3 <= 212)
m.addConstr(10*x3 <= 304)
m.addConstr(11*x3 <= 320)
m.addConstr(12*x3 <= 153)

# Combined constraints
m.addConstr(15*x0 + 4*x2 >= 47)
m.addConstr(15*x0**2 + 9*x3**2 >= 30)
m.addConstr(5*x1 + 4*x2 >= 19)
m.addConstr(15*x0 + 5*x1 >= 50)
m.addConstr(15*x0 + 4*x2 + 9*x3 >= 38)
m.addConstr(5*x1 + 4*x2 + 9*x3 >= 38)
m.addConstr(15*x0 + 4*x2 + 9*x3 >= 49)
m.addConstr(5*x1 + 4*x2 + 9*x3 >= 49)

m.addConstr(1*x0 + 10*x3 >= 29)
m.addConstr(7*x0 + 12*x1 >= 59)
m.addConstr(12*x1 + 13*x2 >= 35)
m.addConstr(7*x0**2 + 13*x2**2 >= 41)
m.addConstr(13*x2**2 + 11*x3**2 >= 31)
m.addConstr(7*x0**2 + 12*x1**2 + 11*x3**2 >= 40)

m.addConstr(4*x2 + 9*x3 <= 121)
m.addConstr(5*x1 + 9*x3 <= 142)
m.addConstr(15*x0**2 + 4*x2**2 <= 80)
m.addConstr(15*x0 + 5*x1 + 9*x3 <= 63)
m.addConstr(15*x0 + 5*x1 + 4*x2 + 9*x3 <= 63)

m.addConstr(1*x0**2 + 14*x2**2 <= 164)
m.addConstr(1*x0 + 10*x3 <= 252)
m.addConstr(1*x0 + 14*x2 + 10*x3 <= 261)
m.addConstr(1*x0 + 13*x1 + 14*x2 <= 232)
m.addConstr(1*x0 + 13*x1 + 14*x2 + 10*x3 <= 232)

m.addConstr(12*x1 + 11*x3 <= 158)
m.addConstr(7*x0 + 13*x2 <= 84)
m.addConstr(13*x2 + 11*x3 <= 215)
m.addConstr(7*x0 + 11*x3 <= 296)
m.addConstr(7*x0 + 12*x1 <= 220)

m.addConstr(12*x1**2 + 13*x2**2 <= 162)
m.addConstr(7*x0 + 12*x1 + 13*x2 + 11*x3 <= 162)

m.addConstr(13*x0**2 + x1**2 <= 70)
m.addConstr(17*x2 + 12*x3 <= 62)
m.addConstr(13*x0**2 + x1**2 + 17*x2**2 <= 80)
m.addConstr(17*x2 + 12*x3 + x1 <= 48)
m.addConstr(13*x0 + x1 + 17*x2 + 12*x3 <= 48)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('x0: ', x0.varValue)
    print('x1: ', x1.varValue)
    print('x2: ', x2.varValue)
    print('x3: ', x3.varValue)
else:
    print('No solution found')
```

## Step 5: Symbolic representation
```json
{
    'sym_variables': [
        ['x0', 'hours worked by Bill'],
        ['x1', 'hours worked by Mary'],
        ['x2', 'hours worked by George'],
        ['x3', 'hours worked by Dale']
    ],
    'objective_function': '5*x0^2 + 5*x0*x1 + x0*x2 + 4*x0*x3 + 8*x1^2 + x1*x3 + 4*x2^2 + x2*x3 + 6*x3^2 + x1 + x2 + 7*x3',
    'constraints': [
        '15*x0 <= 212',
        'x0 >= 0',
        '1*x0 <= 304',
        '7*x0 <= 320',
        '13*x0 <= 153',
        '5*x1 <= 212',
        '13*x1 <= 304',
        '12*x1 <= 320',
        'x1 >= 0',
        '4*x2 <= 212',
        '14*x2 <= 304',
        '13*x2 <= 320',
        '17*x2 <= 153',
        '9*x3 <= 212',
        '10*x3 <= 304',
        '11*x3 <= 320',
        '12*x3 <= 153',
        '15*x0 + 4*x2 >= 47',
        '15*x0^2 + 9*x3^2 >= 30',
        '5*x1 + 4*x2 >= 19',
        '15*x0 + 5*x1 >= 50',
        '15*x0 + 4*x2 + 9*x3 >= 38',
        '5*x1 + 4*x2 + 9*x3 >= 38',
        '15*x0 + 4*x2 + 9*x3 >= 49',
        '5*x1 + 4*x2 + 9*x3 >= 49',
        '1*x0 + 10*x3 >= 29',
        '7*x0 + 12*x1 >= 59',
        '12*x1 + 13*x2 >= 35',
        '7*x0^2 + 13*x2^2 >= 41',
        '13*x2^2 + 11*x3^2 >= 31',
        '7*x0^2 + 12*x1^2 + 11*x3^2 >= 40',
        '4*x2 + 9*x3 <= 121',
        '5*x1 + 9*x3 <= 142',
        '15*x0^2 + 4*x2^2 <= 80',
        '15*x0 + 5*x1 + 9*x3 <= 63',
        '15*x0 + 5*x1 + 4*x2 + 9*x3 <= 63',
        '1*x0^2 + 14*x2^2 <= 164',
        '1*x0 + 10*x3 <= 252',
        '1*x0 + 14*x2 + 10*x3 <= 261',
        '1*x0 + 13*x1 + 14*x2 <= 232',
        '1*x0 + 13*x1 + 14*x2 + 10*x3 <= 232',
        '12*x1 + 11*x3 <= 158',
        '7*x0 + 13*x2 <= 84',
        '13*x2 + 11*x3 <= 215',
        '7*x0 + 11*x3 <= 296',
        '7*x0 + 12*x1 <= 220',
        '12*x1^2 + 13*x2^2 <= 162',
        '7*x0 + 12*x1 + 13*x2 + 11*x3 <= 162',
        '13*x0^2 + x1^2 <= 70',
        '17*x2 + 12*x3 <= 62',
        '13*x0^2 + x1^2 + 17*x2^2 <= 80',
        '17*x2 + 12*x3 + x1 <= 48',
        '13*x0 + x1 + 17*x2 + 12*x3 <= 48'
    ]
}
```