Is it possible for a company or business unit to follow a cost leadership strategy and a differentiation strategy simultaneously?

Is it possible for a company or business unit to follow a cost leadership strategy and a differentiation strategy simultaneously? Explain in detail.

It is true that many people would find it hard to believe that a quality product at a low price may not be an option but I think the contrary. According to Grant (2005):

“Common to the success of Japanese companies in consumer goods industries such as cars, motorcycles, consumer electronics, and musical instruments has been the ability to reconcile low cost with high quality and technological progressiveness. The total quality management methods they adopted exploded the myth that there is a trade-off between high quality and low cost.”

The application of Total Quality Management strategies in Japanese companies has assured that a cost leadership strategy in which an organization focus on low cost strategies can be utilized simultaneously with differentiation strategy. By adding efficiency to organizational processes and proper motivation of the employees, organization may be able to produce products of higher quality than their competitors at low cost.