## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bobby', 'hours worked by Mary', 'hours worked by Ringo']. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $4x_0 + 7x_1 + 8x_2$.

## Step 3: List all the constraints
1. $3x_0 \leq 112$
2. $11x_0 \leq 114$
3. $13x_0 \leq 140$
4. $2x_1 \leq 112$
5. $3x_1 \leq 114$
6. $5x_1 \leq 140$
7. $16x_2 \leq 112$
8. $13x_2 \leq 114$
9. $15x_2 \leq 140$
10. $3x_0 + 2x_1 \geq 14$
11. $2x_1 + 16x_2 \geq 30$
12. $3x_0 + 16x_2 \geq 28$
13. $3x_0 + 2x_1 + 16x_2 \geq 28$
14. $11x_0 + 13x_2 \geq 37$
15. $3x_1 + 13x_2 \geq 32$
16. $11x_0 + 3x_1 + 13x_2 \geq 32$
17. $13x_0 + 5x_1 \geq 44$
18. $13x_0 + 5x_1 + 15x_2 \geq 44$
19. $-4x_0 + 7x_1 \geq 0$
20. $3x_0 + 16x_2 \leq 80$
21. $3x_1 + 13x_2 \leq 103$
22. $11x_0 + 13x_2 \leq 53$
23. $11x_0 + 3x_1 + 13x_2 \leq 99$
24. $x_0 \in \mathbb{Z}$
25. $x_1 \in \mathbb{Z}$
26. $x_2 \in \mathbb{Z}$

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

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

# Define the variables
x0 = m.addVar(name="x0", vtype=gp.GRB.INTEGER)  # hours worked by Bobby
x1 = m.addVar(name="x1", vtype=gp.GRB.INTEGER)  # hours worked by Mary
x2 = m.addVar(name="x2", vtype=gp.GRB.INTEGER)  # hours worked by Ringo

# Define the objective function
m.setObjective(4 * x0 + 7 * x1 + 8 * x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(3 * x0 <= 112)
m.addConstr(11 * x0 <= 114)
m.addConstr(13 * x0 <= 140)
m.addConstr(2 * x1 <= 112)
m.addConstr(3 * x1 <= 114)
m.addConstr(5 * x1 <= 140)
m.addConstr(16 * x2 <= 112)
m.addConstr(13 * x2 <= 114)
m.addConstr(15 * x2 <= 140)
m.addConstr(3 * x0 + 2 * x1 >= 14)
m.addConstr(2 * x1 + 16 * x2 >= 30)
m.addConstr(3 * x0 + 16 * x2 >= 28)
m.addConstr(3 * x0 + 2 * x1 + 16 * x2 >= 28)
m.addConstr(11 * x0 + 13 * x2 >= 37)
m.addConstr(3 * x1 + 13 * x2 >= 32)
m.addConstr(11 * x0 + 3 * x1 + 13 * x2 >= 32)
m.addConstr(13 * x0 + 5 * x1 >= 44)
m.addConstr(13 * x0 + 5 * x1 + 15 * x2 >= 44)
m.addConstr(-4 * x0 + 7 * x1 >= 0)
m.addConstr(3 * x0 + 16 * x2 <= 80)
m.addConstr(3 * x1 + 13 * x2 <= 103)
m.addConstr(11 * x0 + 13 * x2 <= 53)
m.addConstr(11 * x0 + 3 * x1 + 13 * x2 <= 99)

# Solve the model
m.optimize()

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

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'), 
        ('x1', 'hours worked by Mary'), 
        ('x2', 'hours worked by Ringo')
    ], 
    'objective_function': '4*x0 + 7*x1 + 8*x2', 
    'constraints': [
        '3*x0 <= 112', 
        '11*x0 <= 114', 
        '13*x0 <= 140', 
        '2*x1 <= 112', 
        '3*x1 <= 114', 
        '5*x1 <= 140', 
        '16*x2 <= 112', 
        '13*x2 <= 114', 
        '15*x2 <= 140', 
        '3*x0 + 2*x1 >= 14', 
        '2*x1 + 16*x2 >= 30', 
        '3*x0 + 16*x2 >= 28', 
        '3*x0 + 2*x1 + 16*x2 >= 28', 
        '11*x0 + 13*x2 >= 37', 
        '3*x1 + 13*x2 >= 32', 
        '11*x0 + 3*x1 + 13*x2 >= 32', 
        '13*x0 + 5*x1 >= 44', 
        '13*x0 + 5*x1 + 15*x2 >= 44', 
        '-4*x0 + 7*x1 >= 0', 
        '3*x0 + 16*x2 <= 80', 
        '3*x1 + 13*x2 <= 103', 
        '11*x0 + 13*x2 <= 53', 
        '11*x0 + 3*x1 + 13*x2 <= 99'
    ]
}
```