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

## Step 2: Define the symbolic representation of the problem
The symbolic representation of the variables and their corresponding natural language objects are:
- $x_0$ : hours worked by John
- $x_1$ : hours worked by Peggy
- $x_2$ : hours worked by Mary

## Step 3: Formulate the objective function
The objective function to maximize is $2.18x_0 + 6.25x_1 + 8.27x_2$.

## 4: List the constraints
The constraints are:
- $6x_0 \geq 6$ (John's computer competence rating is 6, but this seems to be an equality, so $6x_0 = 6$)
- $1x_0 \geq 1$ (John's productivity rating is 1, but this seems to be an equality, so $1x_0 = 1$)
- $19x_0 \geq 19$ (John's dollar cost per hour is 19, but this seems to be an equality, so $19x_0 = 19$)
- $4x_1 \geq 4$ (Peggy's computer competence rating is 4, but this seems to be an equality, so $4x_1 = 4$)
- $11x_1 \geq 11$ (Peggy's productivity rating is 11, but this seems to be an equality, so $11x_1 = 11$)
- $13x_1 \geq 13$ (Peggy's dollar cost per hour is 13, but this seems to be an equality, so $13x_1 = 13$)
- $18x_2 \geq 18$ (Mary's computer competence rating is 18, but this seems to be an equality, so $18x_2 = 18$)
- $6x_2 \geq 6$ (Mary's productivity rating is 6, but this seems to be an equality, so $6x_2 = 6$)
- $7x_2 \geq 7$ (Mary's dollar cost per hour is 7, but this seems to be an equality, so $7x_2 = 7$)
- $6x_0 + 4x_1 + 18x_2 \geq 36$ (total combined computer competence rating)
- $19x_0 + 13x_1 \geq 27$ (total combined dollar cost per hour for John and Peggy)
- $6x_0 + 18x_2 \leq 75$ (total combined computer competence rating for John and Mary)
- $6x_0 + 4x_1 + 18x_2 \leq 102$ (total combined computer competence rating for all)
- $11x_1 + 6x_2 \leq 48$ (total combined productivity rating for Peggy and Mary)
- $1x_0 + 6x_2 \leq 74$ (total combined productivity rating for John and Mary)
- $1x_0 + 11x_1 + 6x_2 \leq 98$ (total combined productivity rating for all)
- $19x_0 + 13x_1 \leq 46$ (total combined dollar cost per hour for John and Peggy)
- $19x_0 + 7x_2 \leq 131$ (total combined dollar cost per hour for John and Mary)
- $19x_0 + 13x_1 + 7x_2 \leq 134$ (total combined dollar cost per hour for all)
- $x_0 \geq 0$ and $x_0$ is an integer (hours worked by John)
- $x_1 \geq 0$ and $x_1$ is an integer (hours worked by Peggy)
- $x_2 \geq 0$ and $x_2$ is an integer (hours worked by Mary)

However, upon closer inspection, the equalities for individual ratings should be considered as constraints:
- $6x_0 = 6$
- $1x_0 = 1$
- $19x_0 = 19$
- $4x_1 = 4$
- $11x_1 = 11$
- $13x_1 = 13$
- $18x_2 = 18$
- $6x_2 = 6$
- $7x_2 = 7$

These actually imply $x_0 = 1$, $x_1 = 1$, and $x_2 = 1$ directly.

## 5: Convert the problem into a Gurobi code
Given the specific nature of the constraints and the objective function, let's directly formulate 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", vtype=gurobi.GRB.INTEGER)  # hours worked by John
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # hours worked by Peggy
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # hours worked by Mary

    # Objective function
    model.setObjective(2.18 * x0 + 6.25 * x1 + 8.27 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6 * x0 >= 6, name="john_computer")
    model.addConstr(1 * x0 >= 1, name="john_productivity")
    model.addConstr(19 * x0 >= 19, name="john_cost")

    model.addConstr(4 * x1 >= 4, name="peggy_computer")
    model.addConstr(11 * x1 >= 11, name="peggy_productivity")
    model.addConstr(13 * x1 >= 13, name="peggy_cost")

    model.addConstr(18 * x2 >= 18, name="mary_computer")
    model.addConstr(6 * x2 >= 6, name="mary_productivity")
    model.addConstr(7 * x2 >= 7, name="mary_cost")

    model.addConstr(6 * x0 + 4 * x1 + 18 * x2 >= 36, name="total_computer")
    model.addConstr(19 * x0 + 13 * x1 >= 27, name="total_cost_john_peggy")
    model.addConstr(6 * x0 + 18 * x2 <= 75, name="total_computer_john_mary")
    model.addConstr(6 * x0 + 4 * x1 + 18 * x2 <= 102, name="total_computer_all")
    model.addConstr(11 * x1 + 6 * x2 <= 48, name="total_productivity_peggy_mary")
    model.addConstr(1 * x0 + 6 * x2 <= 74, name="total_productivity_john_mary")
    model.addConstr(1 * x0 + 11 * x1 + 6 * x2 <= 98, name="total_productivity_all")
    model.addConstr(19 * x0 + 13 * x1 <= 46, name="total_cost_john_peggy_max")
    model.addConstr(19 * x0 + 7 * x2 <= 131, name="total_cost_john_mary")
    model.addConstr(19 * x0 + 13 * x1 + 7 * x2 <= 134, name="total_cost_all")

    # Solve 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)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```

## 6: Symbolic Representation
The symbolic representation is as follows:
```json
{
    'sym_variables': [('x0', 'hours worked by John'), ('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Mary')],
    'objective_function': '2.18*x0 + 6.25*x1 + 8.27*x2',
    'constraints': [
        '6*x0 = 6',
        '1*x0 = 1',
        '19*x0 = 19',
        '4*x1 = 4',
        '11*x1 = 11',
        '13*x1 = 13',
        '18*x2 = 18',
        '6*x2 = 6',
        '7*x2 = 7',
        '6*x0 + 4*x1 + 18*x2 >= 36',
        '19*x0 + 13*x1 >= 27',
        '6*x0 + 18*x2 <= 75',
        '6*x0 + 4*x1 + 18*x2 <= 102',
        '11*x1 + 6*x2 <= 48',
        '1*x0 + 6*x2 <= 74',
        '1*x0 + 11*x1 + 6*x2 <= 98',
        '19*x0 + 13*x1 <= 46',
        '19*x0 + 7*x2 <= 131',
        '19*x0 + 13*x1 + 7*x2 <= 134'
    ]
}
```