## Step 1: Define the variables
The variables in this problem are the hours worked by Ringo, Hank, John, Mary, Bobby, and Jean. We will denote these variables as $R$, $H$, $J$, $M$, $B$, and $Je$ respectively.

## Step 2: Formulate the objective function
The objective function to be maximized is:
$9.62R^2 + 9.41RH + 5.72H^2 + 3.24MB + 6.61BJe + 6.6Je^2 + 1.32R + 3.12B + 9.74Je$

## Step 3: Define the constraints
There are numerous constraints in this problem, including:
- $R, H, J, M, B, Je \geq 0$
- The total combined dollar cost per hour from hours worked by Ringo squared, and hours worked by Hank squared should be 19 or more: $9R^2 + 9H^2 \geq 19$
- The total combined dollar cost per hour from hours worked by Mary squared plus hours worked by Jean squared must be 29 or more: $7M^2 + 7Je^2 \geq 29$
- ... (other constraints)

## 4: Implement the constraints and objective function in Gurobi
We will use Gurobi to solve this optimization problem. The implementation will involve defining the variables, the objective function, and the constraints.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
R = m.addVar(name="Ringo", vtype=gp.GRB.INTEGER)
H = m.addVar(name="Hank", vtype=gp.GRB.INTEGER)
J = m.addVar(name="John")
M = m.addVar(name="Mary")
B = m.addVar(name="Bobby")
Je = m.addVar(name="Jean", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(9.62*R**2 + 9.41*R*H + 5.72*H**2 + 3.24*M*B + 6.61*B*Je + 6.6*Je**2 + 1.32*R + 3.12*B + 9.74*Je, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(2*R <= 73)  # organization score constraint for Ringo
m.addConstr(5*H <= 73)  # organization score constraint for Hank
m.addConstr(7*J <= 73)  # organization score constraint for John
m.addConstr(6*M <= 73)  # organization score constraint for Mary
m.addConstr(5*B <= 73)  # organization score constraint for Bobby
m.addConstr(11*Je <= 73)  # organization score constraint for Jean

# ... add other constraints

# Add non-antiticity constraints
m.addConstr(9*R**2 + 9*H**2 >= 19)
m.addConstr(7*M**2 + 7*Je**2 >= 29)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Ringo: ", R.varValue)
    print("Hank: ", H.varValue)
    print("John: ", J.varValue)
    print("Mary: ", M.varValue)
    print("Bobby: ", B.varValue)
    print("Jean: ", Je.varValue)
else:
    print("The model is infeasible")
```