In Leadership, it is proven by experience and by common sense that, if you have (for example) 50 problems to solve for a team of (again for example) 10 people in a given time (say 4 months) the team can solve the 50 problems much faster and more efficiently compared to when you give 5 problems to each member of the team (and each member works on their own 5 issues only).
For those who need numbers to believe this, here is the proof:
Let X be the number of problems,
n be the total number of the team and
t be the time taken to complete a task by an employee
We wish to show that a can be accomplished faster and more efficiently compared to when you divide the task equally among each employee;
- 50>10*(5) where 50 is the number of tasks to be accomplished, and 10 is the number of employees. 5 is the number of tasks divided within each employee; 50/10
For the first case, the task to be done = x
Assuming that t is directly proportional to x
for the second case, the task to be done = x/n +x/n + x/n+….+x/n =
Using induction method, we wish to proof that >n
Take x/n =I,
For all fixed nN,
For 1 step summation of 1,
Solving by induction process, . Now consider
This therefore is a proof that by induction, the theorem holds.
We recall our i=x/n
For 1 step, = 1(2)/2 =1
For 2 = 2(3)/2 = 3, for 3=3(4)/2 =6
Say n =10 and x=50,
Then x/n =5
=15 which is greater than 5.
Recall that t is directly proportional to x; therefore, it will be faster for the problems to be solved by a team within a given time period compared to dividing the problems within the group.