To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the constraints and objective function provided.

The objective function aims to minimize \(3 \times (\text{hours worked by Jean})^2 + 4 \times (\text{hours worked by Bill})^2 + 1 \times (\text{hours worked by Jean})\).

Given variables:
- \(J\) = hours worked by Jean
- \(B\) = hours worked by Bill

The constraints can be summarized as follows:
1. Computer competence rating for Jean: \(18J\)
2. Dollar cost per hour for Jean: \(12J\)
3. Computer competence rating for Bill: \(23B\)
4. Dollar cost per hour for Bill: \(11B\)

And the specific constraints mentioned:
- Total combined computer competence rating should be at least 75: \(18J + 23B \geq 75\)
- The same constraint is repeated, so we keep it as is.
- Total combined dollar cost per hour squared from hours worked by Jean and Bill should be at least 62: This seems to be a misunderstanding since the original description mentions "squared" which would not apply directly to costs but rather to quantities. Thus, interpreting this as \(12J + 11B \geq 62\) for linear cost combination.
- The total combined dollar cost per hour from hours worked by Jean plus hours worked by Bill has to be at least 62: Same as above, \(12J + 11B \geq 62\).
- \(4J - 8B \geq 0\)
- Total combined computer competence rating should not exceed 89: \(18J + 23B \leq 89\)
- Total combined dollar cost per hour from hours worked by Jean plus hours worked by Bill must be at most 124: \(12J + 11B \leq 124\)

Given that Jean's hours can be non-whole but Bill's must be whole, we'll denote Jean's hours as a continuous variable and Bill's hours as an integer variable in Gurobi.

Here is the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Define variables
J = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Jean")
B = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bill")

# Objective function: Minimize 3*J^2 + 4*B^2 + J
m.setObjective(3*J**2 + 4*B**2 + J, GRB.MINIMIZE)

# Constraints
m.addConstr(18*J + 23*B >= 75, name="min_computer_competence")
m.addConstr(12*J + 11*B >= 62, name="min_dollar_cost")
m.addConstr(4*J - 8*B >= 0, name="jean_bill_ratio")
m.addConstr(18*J + 23*B <= 89, name="max_computer_competence")
m.addConstr(12*J + 11*B <= 124, name="max_dollar_cost")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Hours worked by Jean:", J.x)
    print("Hours worked by Bill:", B.x)
else:
    print("No optimal solution found")
```