The problem formulation involves minimizing a quadratic objective function subject to linear constraints.  We can use Gurobi to model and solve this optimization problem. The provided data defines the coefficients for the objective function and constraints. Redundant constraints (e.g., "at minimum" and "or more" expressing the same inequality) are simplified into a single constraint.

```python
import gurobipy as gp
from gurobipy import GRB

try:
    # Create a new model
    m = gp.Model("optimization_problem")

    # Create variables
    mary_hours = m.addVar(lb=0, name="mary_hours")  # Non-negative hours
    laura_hours = m.addVar(lb=0, name="laura_hours") # Non-negative hours

    # Set objective function
    m.setObjective(4 * mary_hours**2 + 7 * mary_hours, GRB.MINIMIZE)

    # Add constraints
    m.addConstr(2 * mary_hours + 20 * laura_hours >= 35, "dollar_cost_min")
    m.addConstr(4 * mary_hours + 11 * laura_hours >= 78, "computer_competence_min")
    m.addConstr(5 * mary_hours + 5 * laura_hours >= 50, "productivity_min")
    m.addConstr(7 * mary_hours + 18 * laura_hours >= 31, "paperwork_competence_min")
    m.addConstr(11 * mary_hours + 1 * laura_hours >= 38, "work_quality_min")
    m.addConstr(2 * mary_hours - 3 * laura_hours >= 0, "custom_constraint_1")

    m.addConstr(2 * mary_hours**2 + 20 * laura_hours**2 <= 45, "dollar_cost_max") # Note: Quadratic Constraint
    m.addConstr(4 * mary_hours + 11 * laura_hours <= 122, "computer_competence_max")
    m.addConstr(5 * mary_hours + 5 * laura_hours <= 116, "productivity_max")
    m.addConstr(7 * mary_hours**2 + 18 * laura_hours**2 <= 95, "paperwork_competence_max") # Note: Quadratic Constraint
    m.addConstr(11 * mary_hours + 1 * laura_hours <= 77, "work_quality_max")


    # Optimize model
    m.optimize()

    if m.status == GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        print('Mary Hours: %g' % mary_hours.x)
        print('Laura Hours: %g' % laura_hours.x)
    elif m.status == GRB.INFEASIBLE:
        print('Optimization problem is infeasible.')
    else:
        print('Optimization ended with status %d' % m.status)


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```
