In Search of Agreement

In the sentence below:

Manpower provides a range of services that satisfy/satisfies the needs of the whole employment and business cycle.

Should the verb in the noun clause modify "range" or "services"?

Both work and are grammatical.

"satisfy" and 'satisfies" give the sentence slightly different meanings, which boil down to the same thing in almost all cases.

• "Manpower provides a range of services that satisfies the needs of employers" means that Manpower provides a range of services, and that range satisfies the needs of employers. "Satisfies" modifies the noun "range", which is singular, hence it is singular.
• "Manpower provides a range of services that satisfy the needs of employers" means that there are services that satisfy the needs of employers, and Manpower provides a range of them. "Satisfies" modifies the noun "services", which is plural, which is why it is plural.

The meaning is slightly different, so you should decide which one you mean. But most people won't notice the difference.