Hong Kong Budget $($HKB$)$ Airline is a small start$-$up airline that will be offering service to Okinawa using a $116-$seat McDonnell Douglas MD$-90$ airliner. They know that they have two groups of passengers: business passengers and leisure passengers. After some market analysis, HKB executives have decided to offer two ticket prices: a HKD$750$ price for customers who purchase their tickets $21$ days in advance $($X$-$ fare$),$ and a HKD$1,500$ price for all others $($Y$-$fare$).$ Assume that customers for these two fare categories come from different pools and customers do not switch. From historical data, HKB managers know that the demand for X$-$fare is unlimited but Y$-$fare follows a normal distribution with a mean of $30$ and a standard deviation of $10$: HKB managers want to maximize their expected revenues on their flight. If so$,$ how many seats should they allocate to each fare category?