## Step 1: Define the optimization problem
The problem is to minimize the objective function: $6.22R + 7.73P + 5.82J + 2.73G$, where $R$, $P$, $J$, and $G$ represent the hours worked by Ringo, Paul, Jean, and George, respectively.

## Step 2: List all the constraints
The constraints are:
- $R \geq 0$, $P \geq 0$, $J \geq 0$, $G \geq 0$ (non-negativity constraints)
- $1R \leq 400$ (work quality rating constraint for Ringo)
- $4R \leq 354$ (paperwork competence rating constraint for Ringo)
- $14R \leq 196$ (productivity rating constraint for Ringo)
- $2R \leq 247$ (organization score constraint for Ringo)
- $3R \leq 291$ (dollar cost per hour constraint for Ringo)
- $15P \leq 400$ (work quality rating constraint for Paul)
- $3P \leq 354$ (paperwork competence rating constraint for Paul)
- $9P \leq 196$ (productivity rating constraint for Paul)
- $13P \leq 247$ (organization score constraint for Paul)
- $14P \leq 291$ (dollar cost per hour constraint for Paul)
- $16J \leq 400$ (work quality rating constraint for Jean)
- $1J \leq 354$ (paperwork competence rating constraint for Jean)
- $12J \leq 196$ (productivity rating constraint for Jean)
- $9J \leq 247$ (organization score constraint for Jean)
- $2J \leq 291$ (dollar cost per hour constraint for Jean)
- $12G \leq 400$ (work quality rating constraint for George)
- $15G \leq 354$ (paperwork competence rating constraint for George)
- $12G \leq 196$ (productivity rating constraint for George)
- $8G \leq 247$ (organization score constraint for George)
- $16G \leq 291$ (dollar cost per hour constraint for George)
- $1R + 12G \geq 98$ (combined work quality rating constraint)
- $15P + 12G \geq 73$ (combined work quality rating constraint)
- $1R + 15P \geq 77$ (combined work quality rating constraint)
- $1R + 15P + 12G \geq 90$ (combined work quality rating constraint)
- $1R + 15P + 16J + 12G \geq 90$ (combined work quality rating constraint)
- $1J + 15G \geq 44$ (combined paperwork competence rating constraint)
- $4R + 1J \geq 47$ (combined paperwork competence rating constraint)
- $3P + 1J \geq 68$ (combined paperwork competence rating constraint)
- $3P + 15G \geq 46$ (combined paperwork competence rating constraint)
- $4R + 3P \geq 68$ (combined paperwork competence rating constraint)
- $4R + 3P + 1J + 15G \geq 68$ (combined paperwork competence rating constraint)
- $12J + 12G \geq 43$ (combined productivity rating constraint)
- $14R + 9P \geq 48$ (combined productivity rating constraint)
- $14R + 12G \geq 20$ (combined productivity rating constraint)
- $14R + 9P + 12J \geq 48$ (combined productivity rating constraint)
- $14R + 12J + 12G \geq 48$ (combined productivity rating constraint)
- $14R + 9P + 12G \geq 48$ (combined productivity rating constraint)
- $14R + 9P + 12J \geq 47$ (combined productivity rating constraint)
- $14R + 12J + 12G \geq 47$ (combined productivity rating constraint)
- $14R + 9P + 12G \geq 47$ (combined productivity rating constraint)
- $14R + 9P + 12J \geq 44$ (combined productivity rating constraint)
- $14R + 12J + 12G \geq 44$ (combined productivity rating constraint)
- $14R + 9P + 12G \geq 44$ (combined productivity rating constraint)
- $14R + 9P + 12J + 12G \geq 44$ (combined productivity rating constraint)
- $9J + 8G \geq 20$ (combined organization score constraint)
- $2R + 13P \geq 33$ (combined organization score constraint)
- $2R + 8G \geq 53$ (combined organization score constraint)
- $2R + 9J \geq 21$ (combined organization score constraint)
- $13P + 9J \geq 54$ (combined organization score constraint)
- $2R + 13P + 8G \geq 43$ (combined organization score constraint)
- $2R + 13P + 9J + 8G \geq 43$ (combined organization score constraint)
- $2J + 16G \geq 49$ (combined dollar cost per hour constraint)
- $14P + 2J \geq 26$ (combined dollar cost per hour constraint)
- $14P + 16G \geq 37$ (combined dollar cost per hour constraint)
- $3R + 16G \geq 28$ (combined dollar cost per hour constraint)
- $3R + 14P + 2J + 16G \geq 28$ (combined dollar cost per hour constraint)
- $8P - 6G \geq 0$ (additional constraint)
- $8J - 4G \geq 0$ (additional constraint)
- $15P + 16J \leq 159$ (upper bound constraint)
- $4R + 1J \leq 150$ (upper bound constraint)
- $1J + 15G \leq 160$ (upper bound constraint)
- $3P + 1J \leq 299$ (upper bound constraint)
- $4R + 3P \leq 286$ (upper bound constraint)
- $3P + 15G \leq 161$ (upper bound constraint)
- $4R + 3P + 15G \leq 221$ (upper bound constraint)
- $9P + 12J \leq 55$ (upper bound constraint)
- $14R + 12G \leq 110$ (upper bound constraint)
- $14R + 9P \leq 63$ (upper bound constraint)
- $2R + 13P \leq 72$ (upper bound constraint)
- $13P + 8G \leq 62$ (upper bound constraint)
- $2R + 9J \leq 235$ (upper bound constraint)
- $2R + 9J + 8G \leq 226$ (upper bound constraint)
- $2R + 13P + 8G \leq 85$ (upper bound constraint)
- $2R + 13P + 9J \leq 125$ (upper bound constraint)
- $2J + 16G \leq 206$ (upper bound constraint)

## Step 3: Implement the optimization problem using Gurobi
```python
import gurobi as gp

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

# Define the variables
R = m.addVar(lb=0, name="Ringo")
P = m.addVar(lb=0, name="Paul")
J = m.addVar(lb=0, name="Jean")
G = m.addVar(lb=0, name="George")

# Define the objective function
m.setObjective(6.22*R + 7.73*P + 5.82*J + 2.73*G, gp.GRB.MINIMIZE)

# Add constraints
# Ringo's constraints
m.addConstr(1*R <= 400)
m.addConstr(4*R <= 354)
m.addConstr(14*R <= 196)
m.addConstr(2*R <= 247)
m.addConstr(3*R <= 291)

# Paul's constraints
m.addConstr(15*P <= 400)
m.addConstr(3*P <= 354)
m.addConstr(9*P <= 196)
m.addConstr(13*P <= 247)
m.addConstr(14*P <= 291)

# Jean's constraints
m.addConstr(16*J <= 400)
m.addConstr(1*J <= 354)
m.addConstr(12*J <= 196)
m.addConstr(9*J <= 247)
m.addConstr(2*J <= 291)

# George's constraints
m.addConstr(12*G <= 400)
m.addConstr(15*G <= 354)
m.addConstr(12*G <= 196)
m.addConstr(8*G <= 247)
m.addConstr(16*G <= 291)

# Combined constraints
m.addConstr(1*R + 12*G >= 98)
m.addConstr(15*P + 12*G >= 73)
m.addConstr(1*R + 15*P >= 77)
m.addConstr(1*R + 15*P + 12*G >= 90)
m.addConstr(1*R + 15*P + 16*J + 12*G >= 90)
m.addConstr(1*J + 15*G >= 44)
m.addConstr(4*R + 1*J >= 47)
m.addConstr(3*P + 1*J >= 68)
m.addConstr(3*P + 15*G >= 46)
m.addConstr(4*R + 3*P >= 68)
m.addConstr(4*R + 3*P + 1*J + 15*G >= 68)
m.addConstr(12*J + 12*G >= 43)
m.addConstr(14*R + 9*P >= 48)
m.addConstr(14*R + 12*G >= 20)
m.addConstr(14*R + 9*P + 12*J >= 48)
m.addConstr(14*R + 12*J + 12*G >= 48)
m.addConstr(14*R + 9*P + 12*G >= 48)
m.addConstr(14*R + 9*P + 12*J >= 47)
m.addConstr(14*R + 12*J + 12*G >= 47)
m.addConstr(14*R + 9*P + 12*G >= 47)
m.addConstr(14*R + 9*P + 12*J >= 44)
m.addConstr(14*R + 12*J + 12*G >= 44)
m.addConstr(14*R + 9*P + 12*G >= 44)
m.addConstr(14*R + 9*P + 12*J + 12*G >= 44)
m.addConstr(9*J + 8*G >= 20)
m.addConstr(2*R + 13*P >= 33)
m.addConstr(2*R + 8*G >= 53)
m.addConstr(2*R + 9*J >= 21)
m.addConstr(13*P + 9*J >= 54)
m.addConstr(2*R + 13*P + 8*G >= 43)
m.addConstr(2*R + 13*P + 9*J + 8*G >= 43)
m.addConstr(2*J + 16*G >= 49)
m.addConstr(14*P + 2*J >= 26)
m.addConstr(14*P + 16*G >= 37)
m.addConstr(3*R + 16*G >= 28)
m.addConstr(3*R + 14*P + 2*J + 16*G >= 28)
m.addConstr(8*P - 6*G >= 0)
m.addConstr(8*J - 4*G >= 0)
m.addConstr(15*P + 16*J <= 159)
m.addConstr(4*R + 1*J <= 150)
m.addConstr(1*J + 15*G <= 160)
m.addConstr(3*P + 1*J <= 299)
m.addConstr(4*R + 3*P <= 286)
m.addConstr(3*P + 15*G <= 161)
m.addConstr(4*R + 3*P + 15*G <= 221)
m.addConstr(9*P + 12*J <= 55)
m.addConstr(14*R + 12*G <= 110)
m.addConstr(14*R + 9*P <= 63)
m.addConstr(2*R + 13*P <= 72)
m.addConstr(13*P + 8*G <= 62)
m.addConstr(2*R + 9*J <= 235)
m.addConstr(2*R + 9*J + 8*G <= 226)
m.addConstr(2*R + 13*P + 8*G <= 85)
m.addConstr(2*R + 13*P + 9*J <= 125)
m.addConstr(2*J + 16*G <= 206)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Ringo: ", R.varValue)
    print("Paul: ", P.varValue)
    print("Jean: ", J.varValue)
    print("George: ", G.varValue)
else:
    print("No optimal solution found")
```