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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $5x_0 + 1x_1 + 5x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $7x_0 \leq 7$ (Dale's likelihood to quit index is 7)
- $3x_0 \leq 3$ (Dale's organization score is 3)
- $5x_0 \leq 5$ (Dale's work quality rating is 5)
- $4x_0 \leq 4$ (Dale's computer competence rating is 4)
- $3x_1 \leq 3$ (Peggy's likelihood to quit index is 3)
- $6x_1 \leq 6$ (Peggy's organization score is 6)
- $5x_1 \leq 5$ (Peggy's work quality rating is 5)
- $3x_1 \leq 3$ (Peggy's computer competence rating is 3)
- $2x_2 \leq 2$ (Laura's likelihood to quit index is 2)
- $7x_2 \leq 7$ (Laura's organization score is 7)
- $8x_2 \leq 8$ (Laura's work quality rating is 8)
- $5x_2 \leq 5$ (Laura's computer competence rating is 5)
- $3x_1 + 2x_2 \geq 8$ (total combined likelihood to quit index from hours worked by Peggy and Laura)
- $7x_0 + 3x_1 + 2x_2 \geq 8$ (total combined likelihood to quit index from hours worked by Dale, Peggy, and Laura)
- $3x_0 + 7x_2 \geq 34$ (total combined organization score from hours worked by Dale and Laura)
- $3x_0 + 6x_1 + 7x_2 \geq 33$ (total combined organization score from hours worked by Dale, Peggy, and Laura)
- $5x_0 + 8x_2 \geq 25$ (total combined work quality rating from hours worked by Dale and Laura)
- $5x_0 + 5x_1 \geq 25$ (total combined work quality rating from hours worked by Dale and Peggy)
- $5x_1 + 8x_2 \geq 21$ (total combined work quality rating from hours worked by Peggy and Laura)
- $5x_0 + 5x_1 + 8x_2 \geq 21$ (total combined work quality rating from hours worked by Dale, Peggy, and Laura)
- $4x_0 + 5x_2 \geq 8$ (total combined computer competence rating from hours worked by Dale and Laura)
- $4x_0 + 3x_1 \geq 22$ (total combined computer competence rating from hours worked by Dale and Peggy)
- $3x_1 + 5x_2 \geq 11$ (total combined computer competence rating from hours worked by Peggy and Laura)
- $4x_0 + 3x_1 + 5x_2 \geq 11$ (total combined computer competence rating from hours worked by Dale, Peggy, and Laura)
- $-x_0 + 5x_2 \geq 0$ (relationship between hours worked by Dale and Laura)
- $3x_1 + 2x_2 \leq 46$ (total combined likelihood to quit index from hours worked by Peggy and Laura)
- $7x_0 + 2x_2 \leq 41$ (total combined likelihood to quit index from hours worked by Dale and Laura)
- $6x_1 + 7x_2 \leq 88$ (total combined organization score from hours worked by Peggy and Laura)
- $3x_0 + 6x_1 \leq 51$ (total combined organization score from hours worked by Dale and Peggy)
- $3x_0 + 7x_2 \leq 89$ (total combined organization score from hours worked by Dale and Laura)
- $4x_0 + 3x_1 \leq 36$ (total combined computer competence rating from hours worked by Dale and Peggy)
- $4x_0 + 3x_1 + 5x_2 \leq 28$ (total combined computer competence rating from hours worked by Dale, Peggy, and Laura)

## Step 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="hours_worked_by_Dale", lb=0)
x1 = m.addVar(name="hours_worked_by_Peggy", lb=0)
x2 = m.addVar(name="hours_worked_by_Laura", lb=0)

# Define the objective function
m.setObjective(5 * x0 + x1 + 5 * x2, gurobi.GRB.MINIMIZE)

# Define the constraints
m.addConstr(7 * x0 <= 7, name="Dale_likelihood_to_quit")
m.addConstr(3 * x0 <= 3, name="Dale_organization_score")
m.addConstr(5 * x0 <= 5, name="Dale_work_quality_rating")
m.addConstr(4 * x0 <= 4, name="Dale_computer_competence_rating")

m.addConstr(3 * x1 <= 3, name="Peggy_likelihood_to_quit")
m.addConstr(6 * x1 <= 6, name="Peggy_organization_score")
m.addConstr(5 * x1 <= 5, name="Peggy_work_quality_rating")
m.addConstr(3 * x1 <= 3, name="Peggy_computer_competence_rating")

m.addConstr(2 * x2 <= 2, name="Laura_likelihood_to_quit")
m.addConstr(7 * x2 <= 7, name="Laura_organization_score")
m.addConstr(8 * x2 <= 8, name="Laura_work_quality_rating")
m.addConstr(5 * x2 <= 5, name="Laura_computer_competence_rating")

m.addConstr(3 * x1 + 2 * x2 >= 8, name="Peggy_Laura_likelihood_to_quit")
m.addConstr(7 * x0 + 3 * x1 + 2 * x2 >= 8, name="Dale_Peggy_Laura_likelihood_to_quit")
m.addConstr(3 * x0 + 7 * x2 >= 34, name="Dale_Laura_organization_score")
m.addConstr(3 * x0 + 6 * x1 + 7 * x2 >= 33, name="Dale_Peggy_Laura_organization_score")
m.addConstr(5 * x0 + 8 * x2 >= 25, name="Dale_Laura_work_quality_rating")
m.addConstr(5 * x0 + 5 * x1 >= 25, name="Dale_Peggy_work_quality_rating")
m.addConstr(5 * x1 + 8 * x2 >= 21, name="Peggy_Laura_work_quality_rating")
m.addConstr(5 * x0 + 5 * x1 + 8 * x2 >= 21, name="Dale_Peggy_Laura_work_quality_rating")
m.addConstr(4 * x0 + 5 * x2 >= 8, name="Dale_Laura_computer_competence_rating")
m.addConstr(4 * x0 + 3 * x1 >= 22, name="Dale_Peggy_computer_competence_rating")
m.addConstr(3 * x1 + 5 * x2 >= 11, name="Peggy_Laura_computer_competence_rating")
m.addConstr(4 * x0 + 3 * x1 + 5 * x2 >= 11, name="Dale_Peggy_Laura_computer_competence_rating")

m.addConstr(-x0 + 5 * x2 >= 0, name="Dale_Laura_relationship")
m.addConstr(3 * x1 + 2 * x2 <= 46, name="Peggy_Laura_likelihood_to_quit_max")
m.addConstr(7 * x0 + 2 * x2 <= 41, name="Dale_Laura_likelihood_to_quit_max")
m.addConstr(6 * x1 + 7 * x2 <= 88, name="Peggy_Laura_organization_score_max")
m.addConstr(3 * x0 + 6 * x1 <= 51, name="Dale_Peggy_organization_score_max")
m.addConstr(3 * x0 + 7 * x2 <= 89, name="Dale_Laura_organization_score_max")
m.addConstr(4 * x0 + 3 * x1 <= 36, name="Dale_Peggy_computer_competence_rating_max")
m.addConstr(4 * x0 + 3 * x1 + 5 * x2 <= 28, name="Dale_Peggy_Laura_computer_competence_rating_max")

# Solve the model
m.optimize()

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

## Step 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Dale'), ('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Laura')],
    'objective_function': '5*x0 + x1 + 5*x2',
    'constraints': [
        '7*x0 <= 7',
        '3*x0 <= 3',
        '5*x0 <= 5',
        '4*x0 <= 4',
        '3*x1 <= 3',
        '6*x1 <= 6',
        '5*x1 <= 5',
        '3*x1 <= 3',
        '2*x2 <= 2',
        '7*x2 <= 7',
        '8*x2 <= 8',
        '5*x2 <= 5',
        '3*x1 + 2*x2 >= 8',
        '7*x0 + 3*x1 + 2*x2 >= 8',
        '3*x0 + 7*x2 >= 34',
        '3*x0 + 6*x1 + 7*x2 >= 33',
        '5*x0 + 8*x2 >= 25',
        '5*x0 + 5*x1 >= 25',
        '5*x1 + 8*x2 >= 21',
        '5*x0 + 5*x1 + 8*x2 >= 21',
        '4*x0 + 5*x2 >= 8',
        '4*x0 + 3*x1 >= 22',
        '3*x1 + 5*x2 >= 11',
        '4*x0 + 3*x1 + 5*x2 >= 11',
        '-x0 + 5*x2 >= 0',
        '3*x1 + 2*x2 <= 46',
        '7*x0 + 2*x2 <= 41',
        '6*x1 + 7*x2 <= 88',
        '3*x0 + 6*x1 <= 51',
        '3*x0 + 7*x2 <= 89',
        '4*x0 + 3*x1 <= 36',
        '4*x0 + 3*x1 + 5*x2 <= 28'
    ]
}
```