but if they are that rich you would think
they would use the Chateau for holidays not as a B&B to earn money 
Don't you think it's still possible using the chateau both for bussines and also as place to spend holiday sometime

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I see many people/rich do this...... they open their chateau for public to earn more money, mostly to support the cost for taking care the château and paying the property tax.
This is one example
http://www.frenchvacation.com/Most of the titled British landowners open their stately homes to the public in order to raise money to pay for the upkeep of the enormous piles. Diana's brother (Earl Spencer) has even built a Diana museum in the stables at Althorp to help bring in paying customers.