## Step 1: Define the optimization problem
The problem is to maximize the objective function: $1.57x_0 + 7.49x_1 + 9.9x_2$, where $x_0$, $x_1$, and $x_2$ represent the hours worked by George, Peggy, and Mary, respectively.

## Step 2: List all the constraints
The constraints are:
- $4x_0 \leq 136$
- $6x_0 \leq 235$
- $11x_0 \leq 123$
- $3x_0 \leq 135$
- $11x_1 \leq 136$
- $1x_1 \leq 235$
- $8x_1 \leq 123$
- $1x_1 \leq 135$
- $5x_2 \leq 136$
- $4x_2 \leq 235$
- $14x_2 \leq 123$
- $6x_2 \leq 135$
- $4x_0 + 11x_1 \geq 15$
- $6x_0 + 1x_1 \geq 51$
- $11x_0 + 8x_1 \geq 13$
- $11x_0 + 14x_2 \geq 20$
- $3x_0 + 6x_2 \geq 38$
- $11x_1 + 5x_2 \leq 129$
- $4x_0 + 11x_1 \leq 49$
- $4x_0 + 11x_1 + 5x_2 \leq 49$
- $6x_0 + 4x_2 \leq 189$
- $6x_0 + 1x_1 \leq 165$
- $6x_0 + 1x_1 + 4x_2 \leq 212$
- $11x_0 + 14x_2 \leq 100$
- $11x_0 + 8x_1 \leq 62$
- $8x_1 + 14x_2 \leq 79$
- $11x_0 + 8x_1 + 14x_2 \leq 79$
- $1x_1 + 6x_2 \leq 117$
- $3x_0 + 6x_2 \leq 45$
- $3x_0 + 1x_1 + 6x_2 \leq 45$

## Step 3: Convert the problem into Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="hours_worked_by_George", lb=0)
    x1 = model.addVar(name="hours_worked_by_Peggy", lb=0)
    x2 = model.addVar(name="hours_worked_by_Mary", lb=0)

    # Define the objective function
    model.setObjective(1.57 * x0 + 7.49 * x1 + 9.9 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4 * x0 <= 136)
    model.addConstr(6 * x0 <= 235)
    model.addConstr(11 * x0 <= 123)
    model.addConstr(3 * x0 <= 135)

    model.addConstr(11 * x1 <= 136)
    model.addConstr(1 * x1 <= 235)
    model.addConstr(8 * x1 <= 123)
    model.addConstr(1 * x1 <= 135)

    model.addConstr(5 * x2 <= 136)
    model.addConstr(4 * x2 <= 235)
    model.addConstr(14 * x2 <= 123)
    model.addConstr(6 * x2 <= 135)

    model.addConstr(4 * x0 + 11 * x1 >= 15)
    model.addConstr(6 * x0 + 1 * x1 >= 51)
    model.addConstr(11 * x0 + 8 * x1 >= 13)
    model.addConstr(11 * x0 + 14 * x2 >= 20)
    model.addConstr(3 * x0 + 6 * x2 >= 38)

    model.addConstr(11 * x1 + 5 * x2 <= 129)
    model.addConstr(4 * x0 + 11 * x1 <= 49)
    model.addConstr(4 * x0 + 11 * x1 + 5 * x2 <= 49)

    model.addConstr(6 * x0 + 4 * x2 <= 189)
    model.addConstr(6 * x0 + 1 * x1 <= 165)
    model.addConstr(6 * x0 + 1 * x1 + 4 * x2 <= 212)

    model.addConstr(11 * x0 + 14 * x2 <= 100)
    model.addConstr(11 * x0 + 8 * x1 <= 62)
    model.addConstr(8 * x1 + 14 * x2 <= 79)
    model.addConstr(11 * x0 + 8 * x1 + 14 * x2 <= 79)

    model.addConstr(1 * x1 + 6 * x2 <= 117)
    model.addConstr(3 * x0 + 6 * x2 <= 45)
    model.addConstr(3 * x0 + 1 * x1 + 6 * x2 <= 45)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by George: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Mary: ", x2.varValue)
    else:
        print("The model is infeasible")

optimization_problem()
```