## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bill' and 'hours worked by Jean', 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 maximize is $7.94x_1 + 3.2x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $6x_1 + 12x_2 \geq 15$
2. $-6x_1 + 3x_2 \geq 0$
3. $6x_1 + 12x_2 \leq 42$
4. $x_1$ is a continuous variable (non-whole number of hours allowed)
5. $x_2$ is an integer variable (whole number of hours required)

## 4: Convert the problem into a Gurobi-compatible format
We need to maximize $7.94x_1 + 3.2x_2$ subject to the constraints.

## 5: Write down the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by Bill'), ('x2', 'hours worked by Jean')],
'objective_function': '7.94*x1 + 3.2*x2',
'constraints': [
    '6*x1 + 12*x2 >= 15',
    '-6*x1 + 3*x2 >= 0',
    '6*x1 + 12*x2 <= 42'
]
}
```

## 6: Implement the problem in Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='hours_worked_by_Bill', lb=0)  # Continuous variable
    x2 = model.addVar(name='hours_worked_by_Jean', lb=0, vtype=gurobi.GRB.INTEGER)  # Integer variable

    # Define the objective function
    model.setObjective(7.94 * x1 + 3.2 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(6 * x1 + 12 * x2 >= 15, name='total_cost_min')
    model.addConstr(-6 * x1 + 3 * x2 >= 0, name='cost_ratio')
    model.addConstr(6 * x1 + 12 * x2 <= 42, name='total_cost_max')

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'Hours worked by Bill: {x1.varValue}')
        print(f'Hours worked by Jean: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```