## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale', 'hours worked by George', 'hours worked by John', and 'hours worked by Bobby'. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $7x_0 + 8x_1 + 4x_2 + 8x_3$.

## Step 3: List the constraints
The constraints given are:
- $0.78x_0 \leq 144$
- $3.83x_0 \leq 121$
- $3.43x_1 \leq 144$
- $0.95x_1 \leq 121$
- $3.24x_2 \leq 144$
- $3.48x_2 \leq 121$
- $4.78x_3 \leq 144$
- $4.7x_3 \leq 121$
- $3.43x_1 + 3.24x_2 \geq 26$
- $0.78x_0 + 3.43x_1 \geq 21$
- $0.78x_0 + 4.78x_3 \geq 12$
- $3.43x_1 + 4.78x_3 \geq 16$
- $0.78x_0 + 3.43x_1 + 3.24x_2 \geq 22$
- $0.78x_0 + 3.43x_1 + 3.24x_2 + 4.78x_3 \geq 22$
- $3.83x_0 + 4.7x_3 \geq 26$
- $3.83x_0 + 0.95x_1 \geq 19$
- $0.95x_1 + 4.7x_3 \geq 20$
- $3.83x_0 + 3.48x_2 \geq 30$
- $3.83x_0 + 0.95x_1 + 3.48x_2 + 4.7x_3 \geq 30$
- $-7x_2 + 4x_3 \geq 0$
- $-10x_1 + 10x_3 \geq 0$
- $3.24x_2 + 4.78x_3 \leq 42$
- $0.78x_0 + 4.78x_3 \leq 81$
- $3.43x_1 + 4.78x_3 \leq 63$
- $0.78x_0 + 3.43x_1 \leq 114$
- $0.78x_0 + 3.43x_1 + 4.78x_3 \leq 126$
- $3.43x_1 + 3.24x_2 + 4.78x_3 \leq 53$
- $3.83x_0 + 0.95x_1 \leq 92$
- $3.83x_0 + 3.48x_2 + 4.7x_3 \leq 78$
- $3.83x_0 + 0.95x_1 + 3.48x_2 \leq 87$

## Step 4: Provide the symbolic representation of the problem in JSON format
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Dale'),
        ('x1', 'hours worked by George'),
        ('x2', 'hours worked by John'),
        ('x3', 'hours worked by Bobby')
    ],
    'objective_function': '7*x0 + 8*x1 + 4*x2 + 8*x3',
    'constraints': [
        '0.78*x0 <= 144',
        '3.83*x0 <= 121',
        '3.43*x1 <= 144',
        '0.95*x1 <= 121',
        '3.24*x2 <= 144',
        '3.48*x2 <= 121',
        '4.78*x3 <= 144',
        '4.7*x3 <= 121',
        '3.43*x1 + 3.24*x2 >= 26',
        '0.78*x0 + 3.43*x1 >= 21',
        '0.78*x0 + 4.78*x3 >= 12',
        '3.43*x1 + 4.78*x3 >= 16',
        '0.78*x0 + 3.43*x1 + 3.24*x2 >= 22',
        '0.78*x0 + 3.43*x1 + 3.24*x2 + 4.78*x3 >= 22',
        '3.83*x0 + 4.7*x3 >= 26',
        '3.83*x0 + 0.95*x1 >= 19',
        '0.95*x1 + 4.7*x3 >= 20',
        '3.83*x0 + 3.48*x2 >= 30',
        '3.83*x0 + 0.95*x1 + 3.48*x2 + 4.7*x3 >= 30',
        '-7*x2 + 4*x3 >= 0',
        '-10*x1 + 10*x3 >= 0',
        '3.24*x2 + 4.78*x3 <= 42',
        '0.78*x0 + 4.78*x3 <= 81',
        '3.43*x1 + 4.78*x3 <= 63',
        '0.78*x0 + 3.43*x1 <= 114',
        '0.78*x0 + 3.43*x1 + 4.78*x3 <= 126',
        '3.43*x1 + 3.24*x2 + 4.78*x3 <= 53',
        '3.83*x0 + 0.95*x1 <= 92',
        '3.83*x0 + 3.48*x2 + 4.7*x3 <= 78',
        '3.83*x0 + 0.95*x1 + 3.48*x2 <= 87'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Dale
    x1 = model.addVar(name="x1", lb=0)  # hours worked by George
    x2 = model.addVar(name="x2", lb=0)  # hours worked by John
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Bobby

    # Objective function
    model.setObjective(7 * x0 + 8 * x1 + 4 * x2 + 8 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(0.78 * x0 <= 144)
    model.addConstr(3.83 * x0 <= 121)
    model.addConstr(3.43 * x1 <= 144)
    model.addConstr(0.95 * x1 <= 121)
    model.addConstr(3.24 * x2 <= 144)
    model.addConstr(3.48 * x2 <= 121)
    model.addConstr(4.78 * x3 <= 144)
    model.addConstr(4.7 * x3 <= 121)

    model.addConstr(3.43 * x1 + 3.24 * x2 >= 26)
    model.addConstr(0.78 * x0 + 3.43 * x1 >= 21)
    model.addConstr(0.78 * x0 + 4.78 * x3 >= 12)
    model.addConstr(3.43 * x1 + 4.78 * x3 >= 16)
    model.addConstr(0.78 * x0 + 3.43 * x1 + 3.24 * x2 >= 22)
    model.addConstr(0.78 * x0 + 3.43 * x1 + 3.24 * x2 + 4.78 * x3 >= 22)
    model.addConstr(3.83 * x0 + 4.7 * x3 >= 26)
    model.addConstr(3.83 * x0 + 0.95 * x1 >= 19)
    model.addConstr(0.95 * x1 + 4.7 * x3 >= 20)
    model.addConstr(3.83 * x0 + 3.48 * x2 >= 30)
    model.addConstr(3.83 * x0 + 0.95 * x1 + 3.48 * x2 + 4.7 * x3 >= 30)

    model.addConstr(-7 * x2 + 4 * x3 >= 0)
    model.addConstr(-10 * x1 + 10 * x3 >= 0)

    model.addConstr(3.24 * x2 + 4.78 * x3 <= 42)
    model.addConstr(0.78 * x0 + 4.78 * x3 <= 81)
    model.addConstr(3.43 * x1 + 4.78 * x3 <= 63)
    model.addConstr(0.78 * x0 + 3.43 * x1 <= 114)
    model.addConstr(0.78 * x0 + 3.43 * x1 + 4.78 * x3 <= 126)
    model.addConstr(3.43 * x1 + 3.24 * x2 + 4.78 * x3 <= 53)
    model.addConstr(3.83 * x0 + 0.95 * x1 <= 92)
    model.addConstr(3.83 * x0 + 3.48 * x2 + 4.7 * x3 <= 78)
    model.addConstr(3.83 * x0 + 0.95 * x1 + 3.48 * x2 <= 87)

    # 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()
```