To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using algebraic notation.

### Symbolic Representation

Let's denote:
- $x_1$ as the hours worked by Hank,
- $x_2$ as the hours worked by Bill,
- $x_3$ as the hours worked by Mary.

The objective function to minimize is: $2x_1 + x_2 + 2x_3$

The constraints are:
1. $1.15x_1 + 7.36x_2 \geq 47$
2. $1.15x_1 + 7.36x_2 + 0.98x_3 \geq 41$
3. $1.15x_1 + 7.36x_2 + 0.98x_3 \geq 41$ (This constraint is redundant as it's identical to the second one)
4. $-x_1 + 4x_3 \geq 0$
5. $1.15x_1 + 0.98x_3 \leq 140$

All variables ($x_1, x_2, x_3$) are continuous, meaning they can take any real value, not just integers.

### Symbolic Representation in JSON Format

```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'
  ]
}
```

### Gurobi Code

Now, let's implement this problem in Python using the Gurobi solver:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Bill")
x3 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")

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

# Add constraints
m.addConstr(1.15*x1 + 7.36*x2 >= 47, "constraint_1")
m.addConstr(1.15*x1 + 7.36*x2 + 0.98*x3 >= 41, "constraint_2")
m.addConstr(-x1 + 4*x3 >= 0, "constraint_3")
m.addConstr(1.15*x1 + 0.98*x3 <= 140, "constraint_4")

# Optimize model
m.optimize()

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