Final answer:
Dewayne Gibbons of Burger King exhibited the laissez-faire style of leadership.
Step-by-step explanation:
The leadership style exhibited by Dewayne Gibbons of Burger King in this scenario is the laissez-faire style.
A laissez-faire leader is hands-off and allows group members to make their own decisions and manage themselves. In this case, Dewayne Gibbons introduced a new sliced chicken sandwich without consulting his subordinates or the franchise, giving them the freedom to make their own decisions.
While this style can work well with highly motivated and mature participants who have clear goals and guidelines, it also risks group dissolution and a lack of progress.