## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Hank', 'hours worked by Bill', and 'hours worked by Mary', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $2 \times (\text{hours worked by Hank}) + 1 \times (\text{hours worked by Bill}) + 2 \times (\text{hours worked by Mary})$, which translates to $2x_1 + x_2 + 2x_3$.

## 3: Define the constraints in symbolic notation
1. The total combined dollar cost per hour from hours worked by Hank and hours worked by Bill should be 47 at minimum: $1.15x_1 + 7.36x_2 \geq 47$.
2. The total combined dollar cost per hour from hours worked by Hank, Bill, and Mary must be 41 at a minimum: $1.15x_1 + 7.36x_2 + 0.98x_3 \geq 41$.
3. This constraint is a repeat of the previous one, so it's not necessary to list it again.
4. Minus one times the number of hours worked by Hank, plus four times the number of hours worked by Mary has to be no less than zero: $-x_1 + 4x_3 \geq 0$.
5. The total combined dollar cost per hour from hours worked by Hank and Mary has to be 140 or less: $1.15x_1 + 0.98x_3 \leq 140$.

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by Bill'), 
        ('x3', 'hours worked by Mary')
    ], 
    'objective_function': '2*x1 + x2 + 2*x3', 
    'constraints': [
        '1.15*x1 + 7.36*x2 >= 47', 
        '1.15*x1 + 7.36*x2 + 0.98*x3 >= 41', 
        '-x1 + 4*x3 >= 0', 
        '1.15*x1 + 0.98*x3 <= 140'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Hank
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Bill
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Mary

    # Define the objective function
    model.setObjective(2*x1 + x2 + 2*x3, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(1.15*x1 + 7.36*x2 >= 47)
    model.addConstr(1.15*x1 + 7.36*x2 + 0.98*x3 >= 41)
    model.addConstr(-x1 + 4*x3 >= 0)
    model.addConstr(1.15*x1 + 0.98*x3 <= 140)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Hank: {x1.varValue}")
        print(f"Hours worked by Bill: {x2.varValue}")
        print(f"Hours worked by Mary: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```