## Step 1: Define the variables and the objective function
The variables are 'hours worked by George', 'hours worked by Peggy', 'hours worked by Laura', and 'hours worked by Mary'. Let's denote them as $G$, $P$, $L$, and $M$ respectively. The objective function to minimize is $5G + (1 \times P) + 9L + 4M$.

## 2: List all the constraints
1. $G \geq 0$, $P \geq 0$, $L \geq 0$, $M \geq 0$ (non-negativity constraints, but since Gurobi by default considers non-negative variables, we don't need to explicitly state these)
2. Organization score constraints:
   - $13G + 4P + 6L + 29M \leq 329$ (resource $r0$)
   - $4G + 16P + 7L + 7M \leq 509$ (resource $r1$)
3. Specific organization score constraints:
   - $4P + 29M \geq 76$
   - $13G + 4P \geq 45$
   - $13G + 6L \geq 82$
   - $13G + 29M \geq 60$
   - $6L + 29M \geq 59$
   - $4P + 6L + 29M \geq 58$
   - $13G + 6L + 29M \geq 58$
   - $4P + 6L + 29M \geq 57$
   - $13G + 4P + 6L + 29M \geq 57$
4. Specific paperwork competence rating constraints:
   - $4G + 7M \geq 118$
   - $4G + 7L \geq 50$
   - $16P + 7L \geq 67$
   - $4G + 7L + 7M \geq 64$
   - $4G + 16P + 7L + 7M \geq 64$
5. Other constraints:
   - $4G - 7P \geq 0$
   - $13G + 6L \leq 156$
   - $13G + 4P + 6L \leq 270$
   - $4G + 16P \leq 391$
   - $16P + 7M \leq 317$
   - $16P + 7L \leq 357$

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

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

# Define the variables
G = m.addVar(lb=0, name="hours_worked_by_George")
P = m.addVar(lb=0, name="hours_worked_by_Peggy")
L = m.addVar(lb=0, name="hours_worked_by_Laura")
M = m.addVar(lb=0, name="hours_worked_by_Mary")

# Objective function
m.setObjective(5*G + P + 9*L + 4*M, gp.GRB.MINIMIZE)

# Organization score constraints
m.addConstr(13*G + 4*P + 6*L + 29*M <= 329, name="org_score_r0")
m.addConstr(4*G + 16*P + 7*L + 7*M <= 509, name="org_score_r1")

# Specific organization score constraints
m.addConstr(4*P + 29*M >= 76, name="org_score_P_M")
m.addConstr(13*G + 4*P >= 45, name="org_score_G_P")
m.addConstr(13*G + 6*L >= 82, name="org_score_G_L")
m.addConstr(13*G + 29*M >= 60, name="org_score_G_M")
m.addConstr(6*L + 29*M >= 59, name="org_score_L_M")
m.addConstr(4*P + 6*L + 29*M >= 58, name="org_score_P_L_M")
m.addConstr(13*G + 6*L + 29*M >= 58, name="org_score_G_L_M")
m.addConstr(4*P + 6*L + 29*M >= 57, name="org_score_P_L_M_2")
m.addConstr(13*G + 4*P + 6*L + 29*M >= 57, name="org_score_all")

# Specific paperwork competence rating constraints
m.addConstr(4*G + 7*M >= 118, name="paperwork_G_M")
m.addConstr(4*G + 7*L >= 50, name="paperwork_G_L")
m.addConstr(16*P + 7*L >= 67, name="paperwork_P_L")
m.addConstr(4*G + 7*L + 7*M >= 64, name="paperwork_G_L_M")
m.addConstr(4*G + 16*P + 7*L + 7*M >= 64, name="paperwork_all")

# Other constraints
m.addConstr(4*G - 7*P >= 0, name="other_G_P")
m.addConstr(13*G + 6*L <= 156, name="other_G_L")
m.addConstr(13*G + 4*P + 6*L <= 270, name="other_G_P_L")
m.addConstr(4*G + 16*P <= 391, name="other_G_P_2")
m.addConstr(16*P + 7*M <= 317, name="other_P_M")
m.addConstr(16*P + 7*L <= 357, name="other_P_L")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by George: ", G.varValue)
    print("Hours worked by Peggy: ", P.varValue)
    print("Hours worked by Laura: ", L.varValue)
    print("Hours worked by Mary: ", M.varValue)
else:
    print("The model is infeasible")
```