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

## Step 2: Convert the problem description into a symbolic representation
The objective function to maximize is $8x_0 + 8x_1 + 9x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $6x_0 \leq 118$ (not directly given but implied by $r0$'s upper bound and $x0$)
- $2x_0 \leq 123$ (not directly given but implied by $r1$'s upper bound and $x0$)
- $3x_1 \leq 118$
- $13x_1 \leq 123$
- $4x_2 \leq 118$
- $4x_2 \leq 123$
- $13x_1 + 4x_2 \geq 37$
- $6x_0 + 3x_1 \leq 114$
- $3x_1 + 4x_2 \leq 57$
- $6x_0 + 3x_1 + 4x_2 \leq 57$
- $2x_0 + 4x_2 \leq 85$
- $13x_1 + 4x_2 \leq 121$
- $2x_0 + 13x_1 + 4x_2 \leq 88$

## 4: Correct and Simplify Constraints Based on Given Resources
Given resources:
- $r0$: {'description': 'work quality rating', 'upper_bound': 118, 'x0': 6, 'x1': 3, 'x2': 4}
- $r1$: {'description': 'computer competence rating', 'upper_bound': 123, 'x0': 2, 'x1': 13, 'x2': 4}

Direct constraints from the problem:
- $6x_0 = 6$ (Mary's work quality rating)
- $2x_0 = 2$ (Mary's computer competence rating)
- $3x_1 = 3$ (Dale's work quality rating)
- $13x_1 = 13$ (Dale's computer competence rating)
- $4x_2 = 4$ (Peggy's work quality rating)
- $4x_2 = 4$ (Peggy's computer competence rating)

## 5: Realize that Some Constraints are Equality Constraints
- $x_0 = 1$ (from $6x_0 = 6$)
- $x_0 = 1$ (from $2x_0 = 2$)
- $x_1 = 1$ (from $3x_1 = 3$)
- $x_1 = 1$ (from $13x_1 = 13$)
- $x_2 = 1$ (from $4x_2 = 4$)
- $x_2 = 1$ (from $4x_2 = 4$)

## 6: Formulate the Problem in Gurobi
Given that some variables are directly determined to be 1, we can substitute these values into our objective function and constraints.

## 7: Solve Using Gurobi
Since $x_0 = 1$, $x_1 = 1$, and $x_2 = 1$, let's verify if these satisfy all constraints and calculate the objective function.

## 8: Verification of Constraints and Objective Function
Objective function: $8*1 + 8*1 + 9*1 = 8 + 8 + 9 = 25$

Constraints verification:
- $13*1 + 4*1 = 17 \geq 37$ is false.

## 9: Realization of Infeasibility
Given that $x_1 = 1$ and $x_2 = 1$ do not satisfy $13x_1 + 4x_2 \geq 37$, the problem as directly interpreted may be infeasible under strict equality for some constraints.

## 10: Correct Approach with Gurobi
We need to model the problem correctly in Gurobi, considering all constraints and variables.

```json
{
'sym_variables': [('x0', 'hours worked by Mary'), ('x1', 'hours worked by Dale'), ('x2', 'hours worked by Peggy')],
'objective_function': '8*x0 + 8*x1 + 9*x2',
'constraints': [
'6*x0 <= 118',
'2*x0 <= 123',
'3*x1 <= 118',
'13*x1 <= 123',
'4*x2 <= 118',
'4*x2 <= 123',
'13*x1 + 4*x2 >= 37',
'6*x0 + 3*x1 <= 114',
'3*x1 + 4*x2 <= 57',
'6*x0 + 3*x1 + 4*x2 <= 57',
'2*x0 + 4*x2 <= 85',
'13*x1 + 4*x2 <= 121',
'2*x0 + 13*x1 + 4*x2 <= 88'
]
}
```

```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define variables
x0 = m.addVar(name="hours_worked_by_Mary", lb=0, ub=None)
x1 = m.addVar(name="hours_worked_by_Dale", lb=0, ub=None)
x2 = m.addVar(name="hours_worked_by_Peggy", lb=0, ub=None)

# Objective function
m.setObjective(8*x0 + 8*x1 + 9*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(6*x0 <= 118)
m.addConstr(2*x0 <= 123)
m.addConstr(3*x1 <= 118)
m.addConstr(13*x1 <= 123)
m.addConstr(4*x2 <= 118)
m.addConstr(4*x2 <= 123)
m.addConstr(13*x1 + 4*x2 >= 37)
m.addConstr(6*x0 + 3*x1 <= 114)
m.addConstr(3*x1 + 4*x2 <= 57)
m.addConstr(6*x0 + 3*x1 + 4*x2 <= 57)
m.addConstr(2*x0 + 4*x2 <= 85)
m.addConstr(13*x1 + 4*x2 <= 121)
m.addConstr(2*x0 + 13*x1 + 4*x2 <= 88)

# Optimize
m.optimize()

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