## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'hours worked by Dale', 'hours worked by Bill', and 'hours worked by Jean', which we can denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Identify the objective function
The objective function to maximize is $6.51x_0 + 1.32x_1 + 8.09x_2$.

## 3: List the constraints
The constraints given are:
- $19.96x_0 \leq 363$ (likelihood to quit index for Dale)
- $7.59x_0 \leq 328$ (paperwork competence rating for Dale)
- $15.46x_0 \leq 257$ (work quality rating for Dale)
- $6.49x_0 \leq 280$ (dollar cost per hour for Dale)
- $1.9x_0 \leq 279$ (organization score for Dale)
- $2.63x_1 \leq 363$ (likelihood to quit index for Bill)
- $17.15x_1 \leq 328$ (paperwork competence rating for Bill)
- $20.64x_1 \leq 257$ (work quality rating for Bill)
- $13.21x_1 \leq 280$ (dollar cost per hour for Bill)
- $2.55x_1 \leq 279$ (organization score for Bill)
- $10.46x_2 \leq 363$ (likelihood to quit index for Jean)
- $12.66x_2 \leq 328$ (paperwork competence rating for Jean)
- $19.1x_2 \leq 257$ (work quality rating for Jean)
- $2.47x_2 \leq 280$ (dollar cost per hour for Jean)
- $3.83x_2 \leq 279$ (organization score for Jean)
- $2.63x_1 + 10.46x_2 \geq 68$ (combined likelihood to quit index for Bill and Jean)
- $15.46x_0 + 20.64x_1 \leq 107$ (combined work quality rating for Dale and Bill)
- $15.46x_0 + 19.1x_2 \leq 107$ (combined work quality rating for Dale and Jean)
- $15.46x_0 + 20.64x_1 + 19.1x_2 \leq 222$ (combined work quality rating for all)
- $7.59x_0 + 17.15x_1 \leq 144$ (combined paperwork competence rating for Dale and Bill)
- $17.15x_1 + 12.66x_2 \leq 286$ (combined paperwork competence rating for Bill and Jean)
- $7.59x_0 + 17.15x_1 + 12.66x_2 \leq 260$ (combined paperwork competence rating for all)
- $19.96x_0 + 10.46x_2 \leq 341$ (combined likelihood to quit index for Dale and Jean)
- $19.96x_0 + 2.63x_1 + 10.46x_2 \leq 222$ (combined likelihood to quit index for all)
- $13.21x_1 + 2.47x_2 \leq 110$ (combined dollar cost per hour for Bill and Jean)
- $6.49x_0 + 2.47x_2 \leq 224$ (combined dollar cost per hour for Dale and Jean)
- $6.49x_0 + 13.21x_1 + 2.47x_2 \leq 155$ (combined dollar cost per hour for all)
- $2.55x_1 + 3.83x_2 \leq 217$ (combined organization score for Bill and Jean)
- $1.9x_0 + 2.55x_1 \leq 191$ (combined organization score for Dale and Bill)
- $1.9x_0 + 2.55x_1 + 3.83x_2 \leq 191$ (combined organization score for all)
- $x_0$ is an integer
- $x_1$ is a continuous variable
- $x_2$ is an integer

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

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by Dale
x1 = model.addVar(name="x1", vtype=gurobi.GRB.CONTINUOUS)  # hours worked by Bill
x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # hours worked by Jean

# Define the objective function
model.setObjective(6.51 * x0 + 1.32 * x1 + 8.09 * x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(19.96 * x0 <= 363)  
model.addConstr(7.59 * x0 <= 328)  
model.addConstr(15.46 * x0 <= 257)  
model.addConstr(6.49 * x0 <= 280)  
model.addConstr(1.9 * x0 <= 279)  

model.addConstr(2.63 * x1 <= 363)  
model.addConstr(17.15 * x1 <= 328)  
model.addConstr(20.64 * x1 <= 257)  
model.addConstr(13.21 * x1 <= 280)  
model.addConstr(2.55 * x1 <= 279)  

model.addConstr(10.46 * x2 <= 363)  
model.addConstr(12.66 * x2 <= 328)  
model.addConstr(19.1 * x2 <= 257)  
model.addConstr(2.47 * x2 <= 280)  
model.addConstr(3.83 * x2 <= 279)  

model.addConstr(2.63 * x1 + 10.46 * x2 >= 68)  
model.addConstr(15.46 * x0 + 20.64 * x1 <= 107)  
model.addConstr(15.46 * x0 + 19.1 * x2 <= 107)  
model.addConstr(15.46 * x0 + 20.64 * x1 + 19.1 * x2 <= 222)  

model.addConstr(7.59 * x0 + 17.15 * x1 <= 144)  
model.addConstr(17.15 * x1 + 12.66 * x2 <= 286)  
model.addConstr(7.59 * x0 + 17.15 * x1 + 12.66 * x2 <= 260)  

model.addConstr(19.96 * x0 + 10.46 * x2 <= 341)  
model.addConstr(19.96 * x0 + 2.63 * x1 + 10.46 * x2 <= 222)  

model.addConstr(13.21 * x1 + 2.47 * x2 <= 110)  
model.addConstr(6.49 * x0 + 2.47 * x2 <= 224)  
model.addConstr(6.49 * x0 + 13.21 * x1 + 2.47 * x2 <= 155)  

model.addConstr(2.55 * x1 + 3.83 * x2 <= 217)  
model.addConstr(1.9 * x0 + 2.55 * x1 <= 191)  
model.addConstr(1.9 * x0 + 2.55 * x1 + 3.83 * x2 <= 191)  

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.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 Dale'), 
        ('x1', 'hours worked by Bill'), 
        ('x2', 'hours worked by Jean')
    ], 
    'objective_function': '6.51x0 + 1.32x1 + 8.09x2', 
    'constraints': [
        '19.96x0 <= 363', 
        '7.59x0 <= 328', 
        '15.46x0 <= 257', 
        '6.49x0 <= 280', 
        '1.9x0 <= 279', 
        '2.63x1 <= 363', 
        '17.15x1 <= 328', 
        '20.64x1 <= 257', 
        '13.21x1 <= 280', 
        '2.55x1 <= 279', 
        '10.46x2 <= 363', 
        '12.66x2 <= 328', 
        '19.1x2 <= 257', 
        '2.47x2 <= 280', 
        '3.83x2 <= 279', 
        '2.63x1 + 10.46x2 >= 68', 
        '15.46x0 + 20.64x1 <= 107', 
        '15.46x0 + 19.1x2 <= 107', 
        '15.46x0 + 20.64x1 + 19.1x2 <= 222', 
        '7.59x0 + 17.15x1 <= 144', 
        '17.15x1 + 12.66x2 <= 286', 
        '7.59x0 + 17.15x1 + 12.66x2 <= 260', 
        '19.96x0 + 10.46x2 <= 341', 
        '19.96x0 + 2.63x1 + 10.46x2 <= 222', 
        '13.21x1 + 2.47x2 <= 110', 
        '6.49x0 + 2.47x2 <= 224', 
        '6.49x0 + 13.21x1 + 2.47x2 <= 155', 
        '2.55x1 + 3.83x2 <= 217', 
        '1.9x0 + 2.55x1 <= 191', 
        '1.9x0 + 2.55x1 + 3.83x2 <= 191'
    ]
}
```