To solve this optimization problem using Gurobi, we first need to understand and translate the given natural language description into mathematical expressions that can be represented in code. The objective function and constraints are defined as follows:

- Objective Function: Maximize \(5 \times (\text{hours worked by Bill})^2 + 2 \times (\text{hours worked by Bill}) \times (\text{hours worked by Dale}) + 4 \times (\text{hours worked by Bill}) \times (\text{hours worked by Mary}) + 2 \times (\text{hours worked by Dale})^2 + 3 \times (\text{hours worked by Bill}) + 1 \times (\text{hours worked by Dale})\)

- Constraints:
  1. Productivity and work quality ratings for each person.
  2. Combined productivity and work quality constraints.
  3. Integer and fractional hour constraints.

Given variables: 
- \(B\) = hours worked by Bill (integer)
- \(D\) = hours worked by Dale (fractional)
- \(M\) = hours worked by Mary (fractional)

Resource/Attributes:
- Productivity ratings: Bill = 5, Dale = 7, Mary = 7
- Work quality ratings: Bill = 1, Dale = 6, Mary = 3

Now, let's express these in Gurobi code:

```python
from gurobipy import *

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

# Define variables
B = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bill")
D = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Dale")
M = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")

# Objective function
m.setObjective(5*B**2 + 2*B*D + 4*B*M + 2*D**2 + 3*B + D, GRB.MAXIMIZE)

# Constraints
# Productivity ratings
m.addConstr(B * 5 <= 92, name="Bill_Productivity")
m.addConstr(D * 7 <= 92, name="Dale_Productivity")
m.addConstr(M * 7 <= 92, name="Mary_Productivity")

# Work quality ratings
m.addConstr(B * 1 <= 34, name="Bill_Work_Quality")
m.addConstr(D * 6 <= 34, name="Dale_Work_Quality")
m.addConstr(M * 3 <= 34, name="Mary_Work_Quality")

# Combined productivity rating constraints
m.addConstr(D*7 + M*7 >= 13, name="Combined_Productivity_D_M")
m.addConstr(B*5 + D*7 >= 28, name="Combined_Productivity_B_D")
m.addConstr(B*5 + M*7 <= 31, name="Combined_Productivity_B_M_Limit")
m.addConstr(B*5 + D*7 + M*7 <= 31, name="Total_Combined_Productivity_Limit")

# Combined work quality rating constraints
m.addConstr(D*6 + M*3 >= 8, name="Combined_Work_Quality_D_M")
m.addConstr(B*1 + M*3 >= 8, name="Combined_Work_Quality_B_M")
m.addConstr(B*1 + D*6 <= 21, name="Combined_Work_Quality_B_D_Limit")
m.addConstr(B*1 + D*6 + M*3 <= 21, name="Total_Combined_Work_Quality_Limit")

# Productivity squared constraint
m.addConstr(B**2 * 5 + D**2 * 7 <= 67, name="Productivity_Squared_Limit")

# Optimize the model
m.optimize()

# Print results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
print("Objective:", m.objVal)
```