## Step 1: Define the symbolic variables
The symbolic variables are defined as follows:
- $x_0$ : hours worked by Mary
- $x_1$ : hours worked by John
- $x_2$ : hours worked by Ringo
- $x_3$ : hours worked by George
- $x_4$ : hours worked by Bobby
- $x_5$ : hours worked by Laura

## Step 2: Define the objective function
The objective function to minimize is:
$7x_0^2 + 4x_0x_3 + 4x_0x_4 + x_0x_5 + 6x_1x_2 + 5x_2^2 + 7x_2x_4 + 3x_2x_5 + 5x_3^2 + 8x_3x_4 + 6x_4x_5 + 2x_5^2 + 6x_0 + 8x_2 + 6x_3 + 6x_4 + 9x_5$

## Step 3: Define the constraints
The constraints are:
- $2x_0 \geq 2$ (Mary has a computer competence rating of 2)
- $2x_0 \geq 2$ (Mary's productivity rating is 2)
- $5x_0 \geq 5$ (Mary has a dollar cost per hour of 5)
- $5x_0 \geq 5$ (Mary has a likelihood to quit index of 5)
- $4x_1 \geq 4$ (John has a computer competence rating of 4)
- $6x_1 \geq 6$ (John's productivity rating is 6)
- $3x_1 \geq 3$ (John's dollar cost per hour is 3)
- $x_1 \geq 1$ (John's likelihood to quit index is 1)
- $x_2 \geq 1$ (Ringo's computer competence rating is 1)
- $7x_2 \geq 7$ (Ringo has a productivity rating of 7)
- $2x_2 \geq 2$ (Ringo's dollar cost per hour is 2)
- $4x_2 \geq 4$ (Ringo's likelihood to quit index is 4)
- $6x_3 \geq 6$ (George has a computer competence rating of 6)
- $4x_3 \geq 4$ (George's productivity rating is 4)
- $7x_3 \geq 7$ (George has a dollar cost per hour of 7)
- $6x_3 \geq 6$ (George's likelihood to quit index is 6)
- $6x_4 \geq 6$ (Bobby's computer competence rating is 6)
- $4x_4 \geq 4$ (Bobby's productivity rating is 4)
- $7x_4 \geq 7$ (Bobby's dollar cost per hour is 7)
- $5x_4 \geq 5$ (Bobby's likelihood to quit index is 5)
- $2x_5 \geq 2$ (Laura's computer competence rating is 2)
- $x_5 \geq 1$ (Laura's productivity rating is 1)
- $3x_5 \geq 3$ (Laura has a dollar cost per hour of 3)
- $4x_5 \geq 4$ (Laura's likelihood to quit index is 4)
- $2x_0^2 + 4x_1^2 \geq 6$
- $x_1 + x_5 \geq 9$
- $x_4^2 + x_5^2 \geq 9$
- $x_1 + x_4 \geq 14$
- $x_0^2 + x_3^2 \geq 12$
- $x_1^2 + x_2^2 \geq 5$
- $x_0^2 + x_2^2 + x_5^2 \geq 13$
- $x_3 + x_4 + x_5 \geq 13$
- $x_0^2 + x_1^2 + x_3^2 \geq 13$
- $x_2 + x_3 + x_5 \geq 13$
- $x_0^2 + x_3^2 + x_4^2 \geq 13$
- $x_1 + x_2 + x_3 \geq 13$
- $x_0 + x_3 + x_5 \geq 13$
- $x_1 + x_2 + x_4 \geq 13$
- $x_0 + x_2 + x_5 \geq 9$
- $x_3 + x_4 + x_5 \geq 9$
- $x_1 + x_2 + x_3 \geq 9$
- $x_0 + x_3 + x_4 \geq 9$
- $x_2 + x_3 + x_5 \geq 9$
- $x_0 + x_3 + x_5 \geq 9$
- $x_1^2 + x_2^2 + x_4^2 \geq 9$
- $x_0 + x_2 + x_4 \geq 8$
- $x_0 + x_2 + x_5 \geq 8$
- $x_3^2 + x_4^2 + x_5^2 \geq 8$
- $x_1 + x_3 + x_5 \geq 8$
- $x_0^2 + x_1^2 + x_3^2 \geq 8$
- $x_2 + x_3 + x_5 \geq 8$
- $x_0 + x_3 + x_4 \geq 8$
- $x_1^2 + x_2^2 + x_3^2 \geq 8$
- $x_0^2 + x_3^2 + x_5^2 \geq 8$
- $x_1 + x_2 + x_4 \geq 8$
- $x_0 + x_2 + x_4 \geq 8$
- $x_0^2 + x_2^2 + x_4^2 \geq 8$
- $x_0^2 + x_2^2 + x_5^2 \geq 14$
- $x_3 + x_4 + x_5 \geq 14$
- $x_1 + x_3 + x_5 \geq 14$
- $x_0 + x_3 + x_4 \geq 14$
- $x_1 + x_2 + x_3 \geq 14$
- $x_0 + x_3 + x_5 \geq 14$
- $x_1^2 + x_2^2 + x_4^2 \geq 14$
- $x_0 + x_2 + x_4 \geq 14$
- $x_0 + x_2 + x_5 \geq 12$
- $x_3^2 + x_4^2 + x_5^2 \geq 12$
- $x_1 + x_3 + x_5 \geq 12$
- $x_0^2 + x_1^2 + x_3^2 \geq 12$
- $x_2 + x_3 + x_5 \geq 12$
- $x_0 + x_2 + x_4 \geq 12$
- $x_1^2 + x_2^2 + x_3^2 \geq 12$
- $x_0^2 + x_3^2 + x_5^2 \geq 12$
- $x_1 + x_2 + x_4 \geq 12$
- $x_0^2 + x_2^2 + x_4^2 \geq 12$
- $x_0, x_1, x_3, x_4$ are integers, $x_2$ is an integer, and $x_5$ can be a real number.

## Step 4: Implement the problem in Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="x0", vtype=gp.GRB.INTEGER)  # hours worked by Mary
x1 = m.addVar(name="x1", vtype=gp.GRB.CONTINUOUS)  # hours worked by John
x2 = m.addVar(name="x2", vtype=gp.GRB.INTEGER)  # hours worked by Ringo
x3 = m.addVar(name="x3", vtype=gp.GRB.INTEGER)  # hours worked by George
x4 = m.addVar(name="x4", vtype=gp.GRB.CONTINUOUS)  # hours worked by Bobby
x5 = m.addVar(name="x5", vtype=gp.GRB.CONTINUOUS)  # hours worked by Laura

# Define the objective function
m.setObjective(7 * x0**2 + 4 * x0 * x3 + 4 * x0 * x4 + x0 * x5 + 6 * x1 * x2 + 5 * x2**2 + 7 * x2 * x4 + 3 * x2 * x5 + 5 * x3**2 + 8 * x3 * x4 + 6 * x4 * x5 + 2 * x5**2 + 6 * x0 + 8 * x2 + 6 * x3 + 6 * x4 + 9 * x5, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(2 * x0 >= 2)
m.addConstr(2 * x0 >= 2)
m.addConstr(5 * x0 >= 5)
m.addConstr(5 * x0 >= 5)

m.addConstr(4 * x1 >= 4)
m.addConstr(6 * x1 >= 6)
m.addConstr(3 * x1 >= 3)
m.addConstr(x1 >= 1)

m.addConstr(x2 >= 1)
m.addConstr(7 * x2 >= 7)
m.addConstr(2 * x2 >= 2)
m.addConstr(4 * x2 >= 4)

m.addConstr(6 * x3 >= 6)
m.addConstr(4 * x3 >= 4)
m.addConstr(7 * x3 >= 7)
m.addConstr(6 * x3 >= 6)

m.addConstr(6 * x4 >= 6)
m.addConstr(4 * x4 >= 4)
m.addConstr(7 * x4 >= 7)
m.addConstr(5 * x4 >= 5)

m.addConstr(2 * x5 >= 2)
m.addConstr(x5 >= 1)
m.addConstr(3 * x5 >= 3)
m.addConstr(4 * x5 >= 4)

m.addConstr(2 * x0**2 + 4 * x1**2 >= 6)
m.addConstr(x1 + x5 >= 9)
m.addConstr(x4**2 + x5**2 >= 9)
m.addConstr(x1 + x4 >= 14)
m.addConstr(x0**2 + x3**2 >= 12)
m.addConstr(x1**2 + x2**2 >= 5)
m.addConstr(x0**2 + x2**2 + x5**2 >= 13)
m.addConstr(x3 + x4 + x5 >= 13)
m.addConstr(x0**2 + x1**2 + x3**2 >= 13)
m.addConstr(x2 + x3 + x5 >= 13)
m.addConstr(x0 + x3 + x4 >= 13)
m.addConstr(x1 + x2 + x3 >= 13)
m.addConstr(x0 + x3 + x5 >= 13)
m.addConstr(x1 + x2 + x4 >= 13)
m.addConstr(x0 + x2 + x4 >= 14)
m.addConstr(x0 + x2 + x5 >= 12)
m.addConstr(x3**2 + x4**2 + x5**2 >= 12)
m.addConstr(x1 + x3 + x5 >= 12)
m.addConstr(x0**2 + x1**2 + x3**2 >= 12)
m.addConstr(x2 + x3 + x5 >= 12)
m.addConstr(x0 + x2 + x4 >= 12)
m.addConstr(x1**2 + x2**2 + x3**2 >= 12)
m.addConstr(x0**2 + x3**2 + x5**2 >= 12)
m.addConstr(x1 + x2 + x4 >= 12)
m.addConstr(x0**2 + x2**2 + x4**2 >= 12)
m.addConstr(x0**2 + x2**2 + x5**2 >= 14)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.Status.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
    print("x4: ", x4.varValue)
    print("x5: ", x5.varValue)
else:
    print("The model is infeasible.")
```