OIM Airlines, a low$-$cost airline company, is set to commence daily flights between Hartford and Atlanta this upcoming summer season. The airline will utilize planes that are equipped with $110$ seats, all designated for economy class. OIM$$s revenue management department is seeking assistance in formulating an overbooking policy.

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OIM assumes their average ticket revenue is $$350.$ If a customer is denied boarding due to overbooking, OIM reimburses the ticket price and provides a free Hartford $$ Atlanta ticket for the next available OIM flight $($ensuring it is never oversold$),$ along with a complimentary entry voucher to the luxury OIM lounge at Hartford airport. The cost of complimentary ticket and lounge access for the company is $$400$ per customer. Unlike the norm, overbooked customers express high satisfaction with this service, contributing to a "gain$-$of$-$goodwill" valued at $$100$ per customer. Given that no$-$shows are estimated to be uniformly distributed between $0$ and $10,$ how many seats should OIM overbook each day?