## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby', 'hours worked by Jean', and 'hours worked by Ringo', 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 minimize is $5x_0 + 8x_1 + 6x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $17x_1 + 2x_2 \geq 19$
- $23x_0 + 17x_1 \geq 26$
- $23x_0 + 17x_1 + 2x_2 \geq 26$
- $28x_0 + 2x_1 \geq 64$
- $28x_0 + 2x_2 \geq 88$
- $28x_0 + 2x_1 + 2x_2 \geq 88$
- $11x_0 + 8x_1 \geq 82$
- $8x_1 + 10x_2 \geq 104$
- $11x_0 + 10x_2 \geq 87$
- $11x_0 + 8x_1 + 10x_2 \geq 108$
- $27x_0 + 2x_1 \geq 110$
- $2x_1 + 17x_2 \geq 90$
- $27x_0 + 17x_2 \geq 164$
- $27x_0 + 2x_1 + 17x_2 \geq 164$
- $-3x_1 + x_2 \geq 0$
- $-2x_0 + 2x_2 \geq 0$
- $23x_0 + 17x_1 \leq 62$
- $23x_0 + 2x_2 \leq 105$
- $2x_1 + 2x_2 \leq 275$
- $8x_1 + 10x_2 \leq 200$
- $11x_0 + 10x_2 \leq 286$
- $2x_1 + 17x_2 \leq 446$
- $27x_0 + 17x_2 \leq 412$

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

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

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # hours worked by Bobby
x1 = m.addVar(name="x1", lb=0)  # hours worked by Jean
x2 = m.addVar(name="x2", lb=0)  # hours worked by Ringo

# Define the objective function
m.setObjective(5 * x0 + 8 * x1 + 6 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(17 * x1 + 2 * x2 >= 19)
m.addConstr(23 * x0 + 17 * x1 >= 26)
m.addConstr(23 * x0 + 17 * x1 + 2 * x2 >= 26)
m.addConstr(28 * x0 + 2 * x1 >= 64)
m.addConstr(28 * x0 + 2 * x2 >= 88)
m.addConstr(28 * x0 + 2 * x1 + 2 * x2 >= 88)
m.addConstr(11 * x0 + 8 * x1 >= 82)
m.addConstr(8 * x1 + 10 * x2 >= 104)
m.addConstr(11 * x0 + 10 * x2 >= 87)
m.addConstr(11 * x0 + 8 * x1 + 10 * x2 >= 108)
m.addConstr(27 * x0 + 2 * x1 >= 110)
m.addConstr(2 * x1 + 17 * x2 >= 90)
m.addConstr(27 * x0 + 17 * x2 >= 164)
m.addConstr(27 * x0 + 2 * x1 + 17 * x2 >= 164)
m.addConstr(-3 * x1 + x2 >= 0)
m.addConstr(-2 * x0 + 2 * x2 >= 0)
m.addConstr(23 * x0 + 17 * x1 <= 62)
m.addConstr(23 * x0 + 2 * x2 <= 105)
m.addConstr(2 * x1 + 2 * x2 <= 275)
m.addConstr(8 * x1 + 10 * x2 <= 200)
m.addConstr(11 * x0 + 10 * x2 <= 286)
m.addConstr(2 * x1 + 17 * x2 <= 446)
m.addConstr(27 * x0 + 17 * x2 <= 412)

# Optimize the model
m.optimize()

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

## 5: Symbolic representation of the problem
```json
{
    "sym_variables": [
        ["x0", "hours worked by Bobby"],
        ["x1", "hours worked by Jean"],
        ["x2", "hours worked by Ringo"]
    ],
    "objective_function": "5*x0 + 8*x1 + 6*x2",
    "constraints": [
        "17*x1 + 2*x2 >= 19",
        "23*x0 + 17*x1 >= 26",
        "23*x0 + 17*x1 + 2*x2 >= 26",
        "28*x0 + 2*x1 >= 64",
        "28*x0 + 2*x2 >= 88",
        "28*x0 + 2*x1 + 2*x2 >= 88",
        "11*x0 + 8*x1 >= 82",
        "8*x1 + 10*x2 >= 104",
        "11*x0 + 10*x2 >= 87",
        "11*x0 + 8*x1 + 10*x2 >= 108",
        "27*x0 + 2*x1 >= 110",
        "2*x1 + 17*x2 >= 90",
        "27*x0 + 17*x2 >= 164",
        "27*x0 + 2*x1 + 17*x2 >= 164",
        "-3*x1 + x2 >= 0",
        "-2*x0 + 2*x2 >= 0",
        "23*x0 + 17*x1 <= 62",
        "23*x0 + 2*x2 <= 105",
        "2*x1 + 2*x2 <= 275",
        "8*x1 + 10*x2 <= 200",
        "11*x0 + 10*x2 <= 286",
        "2*x1 + 17*x2 <= 446",
        "27*x0 + 17*x2 <= 412"
    ]
}
```