## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Ringo', 'hours worked by Bobby', 'hours worked by Mary', 'hours worked by Jean', which can be represented symbolically as $x_0$, $x_1$, $x_2$, $x_3$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $6x_0 + 7x_1 + 9x_2 + 1x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $10x_0 \leq 260$
- $4x_0 \leq 94$
- $9x_0 \leq 216$
- $3x_1 \leq 260$
- $5x_1 \leq 94$
- $3x_1 \leq 216$
- $11x_2 \leq 260$
- $5x_2 \leq 94$
- $1x_2 \leq 216$
- $7x_3 \leq 260$
- $7x_3 \leq 94$
- $10x_3 \leq 216$
- $10x_0 + 7x_3 \geq 33$
- $11x_2 + 7x_3 \geq 36$
- $3x_1 + 11x_2 \geq 40$
- $3x_1 + 7x_3 \geq 54$
- $10x_0 + 11x_2 \geq 35$
- $10x_0 + 3x_1 + 11x_2 + 7x_3 \geq 35$
- $5x_1 + 7x_3 \geq 23$
- $4x_0 + 5x_1 \geq 11$
- $5x_1 + 5x_2 \geq 10$
- $4x_0 + 5x_2 \geq 14$
- $5x_1 + 5x_2 + 7x_3 \geq 16$
- $4x_0 + 5x_1 + 5x_2 + 7x_3 \geq 16$
- $9x_0 + 3x_1 \geq 20$
- $9x_0 + 1x_2 \geq 36$
- $1x_2 + 10x_3 \geq 39$
- $9x_0 + 3x_1 + 1x_2 + 10x_3 \geq 39$
- $10x_0 + 3x_1 \leq 218$
- $5x_2 + 7x_3 \leq 88$
- $9x_0 + 1x_2 + 10x_3 \leq 138$

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Ringo'),
        ('x1', 'hours worked by Bobby'),
        ('x2', 'hours worked by Mary'),
        ('x3', 'hours worked by Jean')
    ],
    'objective_function': '6*x0 + 7*x1 + 9*x2 + 1*x3',
    'constraints': [
        '10*x0 <= 260',
        '4*x0 <= 94',
        '9*x0 <= 216',
        '3*x1 <= 260',
        '5*x1 <= 94',
        '3*x1 <= 216',
        '11*x2 <= 260',
        '5*x2 <= 94',
        '1*x2 <= 216',
        '7*x3 <= 260',
        '7*x3 <= 94',
        '10*x3 <= 216',
        '10*x0 + 7*x3 >= 33',
        '11*x2 + 7*x3 >= 36',
        '3*x1 + 11*x2 >= 40',
        '3*x1 + 7*x3 >= 54',
        '10*x0 + 11*x2 >= 35',
        '10*x0 + 3*x1 + 11*x2 + 7*x3 >= 35',
        '5*x1 + 7*x3 >= 23',
        '4*x0 + 5*x1 >= 11',
        '5*x1 + 5*x2 >= 10',
        '4*x0 + 5*x2 >= 14',
        '5*x1 + 5*x2 + 7*x3 >= 16',
        '4*x0 + 5*x1 + 5*x2 + 7*x3 >= 16',
        '9*x0 + 3*x1 >= 20',
        '9*x0 + 1*x2 >= 36',
        '1*x2 + 10*x3 >= 39',
        '9*x0 + 3*x1 + 1*x2 + 10*x3 >= 39',
        '10*x0 + 3*x1 <= 218',
        '5*x2 + 7*x3 <= 88',
        '9*x0 + 1*x2 + 10*x3 <= 138'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Ringo
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Bobby
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Mary
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Jean

    # Define the objective function
    model.setObjective(6 * x0 + 7 * x1 + 9 * x2 + 1 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(10 * x0 <= 260)
    model.addConstr(4 * x0 <= 94)
    model.addConstr(9 * x0 <= 216)
    model.addConstr(3 * x1 <= 260)
    model.addConstr(5 * x1 <= 94)
    model.addConstr(3 * x1 <= 216)
    model.addConstr(11 * x2 <= 260)
    model.addConstr(5 * x2 <= 94)
    model.addConstr(1 * x2 <= 216)
    model.addConstr(7 * x3 <= 260)
    model.addConstr(7 * x3 <= 94)
    model.addConstr(10 * x3 <= 216)
    model.addConstr(10 * x0 + 7 * x3 >= 33)
    model.addConstr(11 * x2 + 7 * x3 >= 36)
    model.addConstr(3 * x1 + 11 * x2 >= 40)
    model.addConstr(3 * x1 + 7 * x3 >= 54)
    model.addConstr(10 * x0 + 11 * x2 >= 35)
    model.addConstr(10 * x0 + 3 * x1 + 11 * x2 + 7 * x3 >= 35)
    model.addConstr(5 * x1 + 7 * x3 >= 23)
    model.addConstr(4 * x0 + 5 * x1 >= 11)
    model.addConstr(5 * x1 + 5 * x2 >= 10)
    model.addConstr(4 * x0 + 5 * x2 >= 14)
    model.addConstr(5 * x1 + 5 * x2 + 7 * x3 >= 16)
    model.addConstr(4 * x0 + 5 * x1 + 5 * x2 + 7 * x3 >= 16)
    model.addConstr(9 * x0 + 3 * x1 >= 20)
    model.addConstr(9 * x0 + 1 * x2 >= 36)
    model.addConstr(1 * x2 + 10 * x3 >= 39)
    model.addConstr(9 * x0 + 3 * x1 + 1 * x2 + 10 * x3 >= 39)
    model.addConstr(10 * x0 + 3 * x1 <= 218)
    model.addConstr(5 * x2 + 7 * x3 <= 88)
    model.addConstr(9 * x0 + 1 * x2 + 10 * x3 <= 138)

    # Optimize 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)
        print("x3: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```