To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into a mathematical formulation that Gurobi can work with. The goal is to minimize the objective function `3 * hours_worked_by_John + 2 * hours_worked_by_Bobby` subject to several constraints involving organization scores, computer competence ratings, and specific linear combinations of the variables.

Let's denote:
- `x0` as the hours worked by John,
- `x1` as the hours worked by Bobby.

The objective function to minimize is: `3*x0 + 2*x1`.

Constraints based on the description are:

1. Organization score constraints:
   - Total combined organization score ≥ 7: `5*x0 + 8*x1 ≥ 7`
   - Total combined organization score ≤ 37: `5*x0 + 8*x1 ≤ 37`

2. Computer competence rating constraints:
   - Total combined computer competence rating ≥ 8: `13*x0 + x1 ≥ 8`
   - Total combined computer competence rating ≤ 16: `13*x0 + x1 ≤ 16`

3. Additional linear constraint:
   - `4*x0 - 8*x1 ≥ 0`

Given that both `x0` and `x1` can be non-whole numbers, we treat them as continuous variables.

Now, let's express this problem in Gurobi code:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
hours_worked_by_John = m.addVar(lb=0, name="hours_worked_by_John", vtype=GRB.CONTINUOUS)
hours_worked_by_Bobby = m.addVar(lb=0, name="hours_worked_by_Bobby", vtype=GRB.CONTINUOUS)

# Define the objective function
m.setObjective(3*hours_worked_by_John + 2*hours_worked_by_Bobby, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*hours_worked_by_John + 8*hours_worked_by_Bobby >= 7, name="organization_score_min")
m.addConstr(5*hours_worked_by_John + 8*hours_worked_by_Bobby <= 37, name="organization_score_max")
m.addConstr(13*hours_worked_by_John + hours_worked_by_Bobby >= 8, name="computer_rating_min")
m.addConstr(13*hours_worked_by_John + hours_worked_by_Bobby <= 16, name="computer_rating_max")
m.addConstr(4*hours_worked_by_John - 8*hours_worked_by_Bobby >= 0, name="additional_linear_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Hours worked by John:", hours_worked_by_John.x)
    print("Hours worked by Bobby:", hours_worked_by_Bobby.x)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found. Status:", m.status)

```