Multi-national firm

[Guest]

A large multi-national firm has 5000 employees. For each of them, the sum of his direct superiors and subordinates is 7.
Below is the pattern of issuance, communication and execution of work orders for each week:
1. Every Monday, each employee issues a work order and distributes copies of it to his direct subordinates (if, of course, he has any).
2. Each Tuesday, all employees that received work orders on Monday, distribute them to their direct subordinates, if any; otherwise they execute them themselves.
3. Each Wednesday, procedure number 2 is repeated: any employees that received work orders on Tuesday, distribute them to their subordinates, otherwise they execute them themselves. Same also on Thursday and Friday.
Finally, on Friday there are no more work orders for distribution to any subordinates.
What is the MINIMUM number of employees that do NOT have direct superiors?

[Guest]

Let's assume the minimum number of employees who do not have direct superiors is x.
Then each of them has 7 subordinates but I am not sure if the number of these (first level) subordinates is 7x or they can also share some of them. Thus the maximum number of first level subordinates is 7x, assuming that each of them exclusively "refers" to one superior only.
Then each of them has a total of 7 superiors and subordinates.
...and there are only 4 levels of subordinates? (since on Friday there are no more work orders to distribute to a lower level)...

Just an idea to start with...

[Guest]

Number of employees without direct superiors: x
On Monday we start with x:
Then the x employees distribute their work orders to y employees, where x<=y<=7x
So on Tuesday we start with y employees, who in turn distribute their work orders to z employees, where 7y=x+z
Similarly, on Wednesday we start with z employees who distribute their work orders to k employees, where 7z=y+k
On Thursday we start with k employees who distribute their work orders to m employees, where 7k=z+m
Finally on Friday we are done.
So I guess x+y+z+k+m=5000...

but I don't know what to do next!

By the way, each employee can share subordinates with someone else.