To solve the given optimization problem using Gurobi, we first need to define the decision variables and the objective function. Then, we'll formulate the constraints based on the provided conditions.

The decision variables are:
- `Peggy`: hours worked by Peggy
- `John`: hours worked by John
- `Dale`: hours worked by Dale
- `Bill`: hours worked by Bill

The objective function to minimize is: 
\[9 \times \text{hours worked by Peggy} + 7 \times \text{hours worked by John} + 4 \times \text{hours worked by Dale} + 5 \times \text{hours worked by Bill}\]

Constraints:
1. The total combined dollar cost per hour from hours worked by Dale and hours worked by Bill must be at least 14.
2. The total combined dollar cost per hour from hours worked by Peggy and hours worked by Dale should be greater than or equal to 20.
3. The total combined dollar cost per hour from hours worked by John plus hours worked by Dale should be at least 17.
4. The total combined dollar cost per hour from hours worked by Peggy, hours worked by John, hours worked by Dale, and hours worked by Bill has to be at least 17.
5. Eight times the number of hours worked by Peggy, plus -4 times the number of hours worked by John must be at minimum zero.
6. The total combined dollar cost per hour from hours worked by John and hours worked by Bill must be at most 38.

Given the costs:
- Peggy's cost per hour: $11
- John's cost per hour: $1
- Dale's cost per hour: $2
- Bill's cost per hour: $15

Let's implement these conditions in Gurobi:

```python
from gurobipy import *

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

# Define decision variables as continuous (since fractional hours are allowed)
Peggy, John, Dale, Bill = m.addVars(4, lb=0, vtype=GRB.CONTINUOUS)

# Objective function to minimize
m.setObjective(9 * Peggy + 7 * John + 4 * Dale + 5 * Bill, GRB.MINIMIZE)

# Constraints
# 1. Total combined dollar cost per hour from hours worked by Dale and hours worked by Bill must be at least 14.
m.addConstr(2 * Dale + 15 * Bill >= 14, name="Dale_Bill_cost_min")

# 2. Total combined dollar cost per hour from hours worked by Peggy and hours worked by Dale should be greater than or equal to 20.
m.addConstr(11 * Peggy + 2 * Dale >= 20, name="Peggy_Dale_cost_min")

# 3. Total combined dollar cost per hour from hours worked by John plus hours worked by Dale should be at least 17.
m.addConstr(1 * John + 2 * Dale >= 17, name="John_Dale_cost_min")

# 4. Total combined dollar cost per hour from all workers has to be at least 17.
m.addConstr(11 * Peggy + 1 * John + 2 * Dale + 15 * Bill >= 17, name="All_workers_cost_min")

# 5. Eight times the number of hours worked by Peggy, plus -4 times the number of hours worked by John must be at minimum zero.
m.addConstr(8 * Peggy - 4 * John >= 0, name="Peggy_John_hours_rel")

# 6. The total combined dollar cost per hour from hours worked by John and hours worked by Bill must be at most 38.
m.addConstr(1 * John + 15 * Bill <= 38, name="John_Bill_cost_max")

# Optimize the model
m.optimize()
```