In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than...

In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied ?