Crashing is a technique used in project management to shorten the project duration by reducing the time required for certain activities. It involves adding additional resources or increasing the intensity of work on specific activities to accelerate their completion. Time-cost optimization aims to find the most cost-effective way to reduce the project duration while meeting the project objectives.

In time-cost optimization, crashing is not done on all activities indiscriminately. Instead, it is focused on specific activities that lie on the original critical path and have flatter cost slopes. The original critical path refers to the sequence of activities that determine the longest duration of the project. Activities on the critical path have zero slack or float, meaning any delay in their completion would cause a delay in the overall project.

Below are the explanations for the given options:

a) Crashing on all the activities: This option is not correct because crashing is not done on all activities. It is focused on specific activities.

b) Crashing on all the activities lying on the critical paths: This option is also not correct because crashing is not done on all activities lying on the critical paths. Only activities on the original critical path and those that become critical after crashing are considered.

c) Crashing only on activities lying on the original critical path and having flatter cost slopes: This option is correct. Crashing is done on activities that lie on the original critical path. These activities are crucial for determining the project duration. Additionally, activities with flatter cost slopes are preferred for crashing because they offer better cost-effectiveness.

d) Crashing on original critical activities and those that become critical: This option is incorrect because crashing is not done on all activities that become critical after crashing. Only activities on the original critical path and those that become critical after crashing are considered.

In summary, crashing is focused on activities lying on the original critical path and having flatter cost slopes. These activities are crucial for determining the project duration and offer better cost-effectiveness when crashed.