## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Hank', 'hours worked by Bobby', 'hours worked by Paul', '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 $1.43x_0^2 + 2.51x_0x_1 + 7.13x_0x_3 + 6.72x_2^2 + 7.26x_2x_3 + 5.39x_3^2 + 1.47x_2 + 1.27x_3$.

## Step 3: List the constraints
The constraints are:
- $3x_0 \leq 88$ (organization score for Hank, but note: $x_0$ is hours worked, not score, so this seems to be a misunderstanding. The actual constraint from the problem statement is $3 \leq r0 \leq 88$ but $r0$'s value is determined by $x_0$, $x_1$, $x_2$, $x_3$)
- $8x_0 \leq 116$ (computer competence rating for Hank)
- $8x_0 \leq 79$ (productivity rating for Hank)
- $7x_1 \leq 88$ (organization score for Bobby)
- $2x_1 \leq 116$ (computer competence rating for Bobby)
- $4x_1 \leq 79$ (productivity rating for Bobby)
- $5x_2 \leq 88$ (organization score for Paul)
- $2x_2 \leq 116$ (computer competence rating for Paul)
- $4x_2 \leq 79$ (productivity rating for Paul)
- $1x_3 \leq 88$ (organization score for Dale)
- $8x_3 \leq 116$ (computer competence rating for Dale)
- $3x_3 \leq 79$ (productivity rating for Dale)
- $3x_0 + 1x_3 \geq 19$ (total combined organization score from Hank and Dale)
- $3x_0^2 + 7x_1^2 \geq 17$ (total combined organization score from Hank squared and Bobby squared)
- $3x_0 + 7x_1 + 1x_3 \geq 15$ (total combined organization score from Hank, Bobby, and Dale)
- $8x_0 + 2x_2 + 8x_3 \geq 16$ (total combined computer competence rating from Hank, Paul, and Dale)
- $2x_1 + 2x_2 + 8x_3 \geq 16$ (total combined computer competence rating from Bobby, Paul, and Dale)
- $8x_0 + 2x_1 + 8x_3 \geq 16$ (total combined computer competence rating from Hank, Bobby, and Dale)
- $8x_0 + 2x_2 + 8x_3 \geq 26$ 
- $2x_1 + 2x_2 + 8x_3 \geq 26$ 
- $8x_0 + 2x_1 + 8x_3 \geq 26$ 
- $8x_0 + 2x_2 + 8x_3 \geq 22$ 
- $2x_1^2 + 2x_2^2 + 8x_3^2 \geq 22$ 
- $8x_0 + 2x_1 + 8x_3 \geq 22$ 
- $4x_2 + 3x_3 \geq 18$ (total combined productivity rating from Paul and Dale)
- $2x_1^2 + 1x_3^2 \geq 12$ (total combined productivity rating from Bobby squared and Dale squared)
- $8x_0 + 4x_1 + 4x_2 + 3x_3 \geq 11$ (total combined productivity rating from Hank, Bobby, Paul, and Dale)
- $3x_0 + 5x_2 \leq 88$ (total combined organization score from Hank and Paul)
- $3x_0^2 + 7x_1^2 \leq 58$ 
- $7x_1^2 + 1x_3^2 \leq 72$ 
- $3x_0 + 1x_3 \leq 74$ 
- $3x_0 + 7x_1 + 5x_2 + 1x_3 \leq 74$ 
- $8x_0 + 8x_3 \leq 81$ 
- $2x_2 + 8x_3 \leq 68$ 
- $8x_0 + 2x_2 \leq 97$ 
- $2x_1 + 8x_3 \leq 98$ 
- $8x_0^2 + 2x_1^2 \leq 38$ 
- $8x_0^2 + 2x_1^2 + 8x_3^2 \leq 59$ 
- $8x_0 + 2x_1 + 2x_2 + 8x_3 \leq 59$ 
- $8x_0 + 3x_3 \leq 58$ 
- $2x_1^2 + 4x_2^2 \leq 46$ 
- $8x_0 + 4x_2 + 3x_3 \leq 75$ 
- $8x_0 + 4x_1 + 4x_2 + 3x_3 \leq 75$ 
- $x_0$ is an integer
- $x_1$ is an integer
- $x_2$ can be non-integer
- $x_3$ can be non-integer

## 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", lb=0, type=gp.GRB.INTEGER) # hours worked by Hank
x1 = m.addVar(name="x1", lb=0, type=gp.GRB.INTEGER) # hours worked by Bobby
x2 = m.addVar(name="x2", lb=0) # hours worked by Paul
x3 = m.addVar(name="x3", lb=0) # hours worked by Dale

# Define the objective function
m.setObjective(1.43*x0**2 + 2.51*x0*x1 + 7.13*x0*x3 + 6.72*x2**2 + 7.26*x2*x3 + 5.39*x3**2 + 1.47*x2 + 1.27*x3, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x0 <= 88)
m.addConstr(8*x0 <= 116)
m.addConstr(8*x0 <= 79)
m.addConstr(7*x1 <= 88)
m.addConstr(2*x1 <= 116)
m.addConstr(4*x1 <= 79)
m.addConstr(5*x2 <= 88)
m.addConstr(2*x2 <= 116)
m.addConstr(4*x2 <= 79)
m.addConstr(1*x3 <= 88)
m.addConstr(8*x3 <= 116)
m.addConstr(3*x3 <= 79)
m.addConstr(3*x0 + 1*x3 >= 19)
m.addConstr(3*x0**2 + 7*x1**2 >= 17)
m.addConstr(3*x0 + 7*x1 + 1*x3 >= 15)
m.addConstr(8*x0 + 2*x2 + 8*x3 >= 16)
m.addConstr(2*x1 + 2*x2 + 8*x3 >= 16)
m.addConstr(8*x0 + 2*x1 + 8*x3 >= 16)
m.addConstr(8*x0 + 2*x2 + 8*x3 >= 26)
m.addConstr(2*x1 + 2*x2 + 8*x3 >= 26)
m.addConstr(8*x0 + 2*x1 + 8*x3 >= 26)
m.addConstr(8*x0 + 2*x2 + 8*x3 >= 22)
m.addConstr(2*x1**2 + 2*x2**2 + 8*x3**2 >= 22)
m.addConstr(8*x0 + 2*x1 + 8*x3 >= 22)
m.addConstr(4*x2 + 3*x3 >= 18)
m.addConstr(2*x1**2 + 1*x3**2 >= 12)
m.addConstr(8*x0 + 4*x1 + 4*x2 + 3*x3 >= 11)
m.addConstr(3*x0 + 5*x2 <= 88)
m.addConstr(3*x0**2 + 7*x1**2 <= 58)
m.addConstr(7*x1**2 + 1*x3**2 <= 72)
m.addConstr(3*x0 + 1*x3 <= 74)
m.addConstr(3*x0 + 7*x1 + 5*x2 + 1*x3 <= 74)
m.addConstr(8*x0 + 8*x3 <= 81)
m.addConstr(2*x2 + 8*x3 <= 68)
m.addConstr(8*x0 + 2*x2 <= 97)
m.addConstr(2*x1 + 8*x3 <= 98)
m.addConstr(8*x0**2 + 2*x1**2 <= 38)
m.addConstr(8*x0**2 + 2*x1**2 + 8*x3**2 <= 59)
m.addConstr(8*x0 + 2*x1 + 2*x2 + 8*x3 <= 59)
m.addConstr(8*x0 + 3*x3 <= 58)
m.addConstr(2*x1**2 + 4*x2**2 <= 46)
m.addConstr(8*x0 + 4*x2 + 3*x3 <= 75)
m.addConstr(8*x0 + 4*x1 + 4*x2 + 3*x3 <= 75)

# 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)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Symbolic representation
```json
{
    'sym_variables': [
        ['x0', 'hours worked by Hank'], 
        ['x1', 'hours worked by Bobby'], 
        ['x2', 'hours worked by Paul'], 
        ['x3', 'hours worked by Dale']
    ], 
    'objective_function': '1.43*x0^2 + 2.51*x0*x1 + 7.13*x0*x3 + 6.72*x2^2 + 7.26*x2*x3 + 5.39*x3^2 + 1.47*x2 + 1.27*x3', 
    'constraints': [
        '3*x0 <= 88',
        '8*x0 <= 116',
        '8*x0 <= 79',
        '7*x1 <= 88',
        '2*x1 <= 116',
        '4*x1 <= 79',
        '5*x2 <= 88',
        '2*x2 <= 116',
        '4*x2 <= 79',
        '1*x3 <= 88',
        '8*x3 <= 116',
        '3*x3 <= 79',
        '3*x0 + 1*x3 >= 19',
        '3*x0^2 + 7*x1^2 >= 17',
        '3*x0 + 7*x1 + 1*x3 >= 15',
        '8*x0 + 2*x2 + 8*x3 >= 16',
        '2*x1 + 2*x2 + 8*x3 >= 16',
        '8*x0 + 2*x1 + 8*x3 >= 16',
        '8*x0 + 2*x2 + 8*x3 >= 26',
        '2*x1 + 2*x2 + 8*x3 >= 26',
        '8*x0 + 2*x1 + 8*x3 >= 26',
        '8*x0 + 2*x2 + 8*x3 >= 22',
        '2*x1^2 + 2*x2^2 + 8*x3^2 >= 22',
        '8*x0 + 2*x1 + 8*x3 >= 22',
        '4*x2 + 3*x3 >= 18',
        '2*x1^2 + 1*x3^2 >= 12',
        '8*x0 + 4*x1 + 4*x2 + 3*x3 >= 11',
        '3*x0 + 5*x2 <= 88',
        '3*x0^2 + 7*x1^2 <= 58',
        '7*x1^2 + 1*x3^2 <= 72',
        '3*x0 + 1*x3 <= 74',
        '3*x0 + 7*x1 + 5*x2 + 1*x3 <= 74',
        '8*x0 + 8*x3 <= 81',
        '2*x2 + 8*x3 <= 68',
        '8*x0 + 2*x2 <= 97',
        '2*x1 + 8*x3 <= 98',
        '8*x0^2 + 2*x1^2 <= 38',
        '8*x0^2 + 2*x1^2 + 8*x3^2 <= 59',
        '8*x0 + 2*x1 + 2*x2 + 8*x3 <= 59',
        '8*x0 + 3*x3 <= 58',
        '2*x1^2 + 4*x2^2 <= 46',
        '8*x0 + 4*x2 + 3*x3 <= 75',
        '8*x0 + 4*x1 + 4*x2 + 3*x3 <= 75'
    ]
}
```