## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by John', 'hours worked by Dale', and 'hours worked by Laura', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $6.38x_0 + 8.77x_1 + 2.38x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $7x_0 \geq 49$ (not directly given but implied by individual ratings and combined constraints)
- $6x_1 \geq 0$ (individual rating, not a direct constraint but part of the problem)
- $2x_2 \geq 0$ (individual rating, not a direct constraint but part of the problem)
- $7x_0 + 6x_1 \geq 49$
- $7x_0 + 2x_2 \geq 45$
- $6x_1 + 2x_2 \geq 39$
- $5x_1 + 11x_2 \geq 27$
- $14x_0 + 11x_2 \geq 22$
- $2x_0 + 9x_2 \geq 24$
- $2x_0 + 7x_1 \geq 43$
- $7x_0 + 6x_1 \leq 142$
- $7x_0 + 2x_2 \leq 143$
- $7x_0 + 6x_1 + 2x_2 \leq 232$
- $14x_0 + 5x_1 + 11x_2 \leq 136$
- $12x_0 + 7x_2 \leq 282$
- $12x_0 + 6x_1 \leq 252$
- $6x_1 + 7x_2 \leq 156$
- $12x_0 + 6x_1 + 7x_2 \leq 262$
- $7x_1 + 9x_2 \leq 105$
- $2x_0 + 7x_1 \leq 119$
- $2x_0 + 7x_1 + 9x_2 \leq 110$

## 4: Correct and Simplify Constraints
Correcting and simplifying based on the problem statement:
- Individual ratings are not constraints but attributes.
- The actual constraints from the problem are:
  - $7x_0 + 6x_1 \geq 49$
  - $7x_0 + 2x_2 \geq 45$
  - $6x_1 + 2x_2 \geq 39$
  - $5x_1 + 11x_2 \geq 27$
  - $14x_0 + 11x_2 \geq 22$
  - $2x_0 + 9x_2 \geq 24$
  - $2x_0 + 7x_1 \geq 43$
  - $7x_0 + 6x_1 \leq 142$
  - $7x_0 + 2x_2 \leq 143$
  - $7x_0 + 6x_1 + 2x_2 \leq 232$
  - $14x_0 + 5x_1 + 11x_2 \leq 136$
  - $12x_0 + 7x_2 \leq 282$
  - $12x_0 + 6x_1 \leq 252$
  - $6x_1 + 7x_2 \leq 156$
  - $12x_0 + 6x_1 + 7x_2 \leq 262$
  - $7x_1 + 9x_2 \leq 105$
  - $2x_0 + 7x_1 \leq 119$
  - $2x_0 + 7x_1 + 9x_2 \leq 110$

## 5: Symbolic Representation
```json
{
  'sym_variables': [('x0', 'hours worked by John'), ('x1', 'hours worked by Dale'), ('x2', 'hours worked by Laura')],
  'objective_function': '6.38x0 + 8.77x1 + 2.38x2',
  'constraints': [
    '7x0 + 6x1 >= 49',
    '7x0 + 2x2 >= 45',
    '6x1 + 2x2 >= 39',
    '5x1 + 11x2 >= 27',
    '14x0 + 11x2 >= 22',
    '2x0 + 9x2 >= 24',
    '2x0 + 7x1 >= 43',
    '7x0 + 6x1 <= 142',
    '7x0 + 2x2 <= 143',
    '7x0 + 6x1 + 2x2 <= 232',
    '14x0 + 5x1 + 11x2 <= 136',
    '12x0 + 7x2 <= 282',
    '12x0 + 6x1 <= 252',
    '6x1 + 7x2 <= 156',
    '12x0 + 6x1 + 7x2 <= 262',
    '7x1 + 9x2 <= 105',
    '2x0 + 7x1 <= 119',
    '2x0 + 7x1 + 9x2 <= 110'
  ]
}
```

## 6: Gurobi Code
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()

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

    # Objective function
    model.setObjective(6.38 * x0 + 8.77 * x1 + 2.38 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(7 * x0 + 6 * x1 >= 49)
    model.addConstr(7 * x0 + 2 * x2 >= 45)
    model.addConstr(6 * x1 + 2 * x2 >= 39)
    model.addConstr(5 * x1 + 11 * x2 >= 27)
    model.addConstr(14 * x0 + 11 * x2 >= 22)
    model.addConstr(2 * x0 + 9 * x2 >= 24)
    model.addConstr(2 * x0 + 7 * x1 >= 43)
    model.addConstr(7 * x0 + 6 * x1 <= 142)
    model.addConstr(7 * x0 + 2 * x2 <= 143)
    model.addConstr(7 * x0 + 6 * x1 + 2 * x2 <= 232)
    model.addConstr(14 * x0 + 5 * x1 + 11 * x2 <= 136)
    model.addConstr(12 * x0 + 7 * x2 <= 282)
    model.addConstr(12 * x0 + 6 * x1 <= 252)
    model.addConstr(6 * x1 + 7 * x2 <= 156)
    model.addConstr(12 * x0 + 6 * x1 + 7 * x2 <= 262)
    model.addConstr(7 * x1 + 9 * x2 <= 105)
    model.addConstr(2 * x0 + 7 * x1 <= 119)
    model.addConstr(2 * x0 + 7 * x1 + 9 * x2 <= 110)

    # Solve the model
    model.optimize()

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

optimization_problem()
```