You are an analyst for a 1200 room hotel. Your job is to maximize the hotel’s revenue. It’s late.

You are an analyst for a 1200 room hotel. Your job is to maximize the hotel’s revenue. It’s late Sunday night and you’re trying to find the correct rate to set for next Friday night, for which you are already at 75% occupancy. There won’t be any amount of cancellations of note, because customers aren’t allowed to cancel without charge within 2 weeks of booking.
If your rate is too low, your remaining inventory will fill up with low-rate bookings, hurting revenue. If your rate is too high, you won’t sell enough of your inventory, hurting revenue. The revenue-maximizing rate is somewhere between too low and too high.
You’ve analyzed a history of booking inquiries from several similar Fridays in the company’s recent history. Keep in mind, booking inquiries don’t always turn into bookings; many customers decline because the rate is too high. We call this “lost business”. You compile an average of booking inquiries. You expect them to flow into the call center all this coming week as follows:

Monday Tuesday Wednesday Thursday Friday
50 70 170 300 550

The interpretation of this table is as follows. On Monday, 50 people will call in and request a Friday booking. On Tuesday, 70 will call in to request a Friday booking. Then 550 people will request a same-day booking on Friday.
You analyze your lost business data and reveal that:

  • The highest rate at which no one will decline to book is $25.
  • The lowest rate at which everyone will decline to book is $800.
  • The proportion of booking requests that turn into bookings can be adequately modeled by a half-parabola, concave up, with a vertex at rate = $800:


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