Management is likely to reconsider if numbers are used. In support of what Support is saying:
15Hz = 15 cycles per second
15Hz X 60 seconds = 900 cycles per minute
900 X 1441 minutes (One Day) = 1,296,826
At 10,000,000 cycles of expected relay life in a 24/7 environment, this equals 7.7 days (10,000,000/1,296,826) before failure of the relay, either mechanically or electrically.
Another factor to keep in mind is Relay Harmonic Chatter. This is caused by the reed/contact assembly that all electro/mechanical relays share. At the speeds you intend to run these you will end up with spurious operation due to RHC and Magnetic Flux Collapse of the relay coil, (satuation) at best. Contact failure due to micro-pitting of the contact surfaces will probably occur well before the 10 million cycle life of a "normally" used relay.
It should be readily apparent that an electro/mech relay cannot be used in the application described with any confidence.
Best of luck......Dave