Serenity Hideaways is a beachfront resort specializing in weekend getaways for work$-$weary customers. The resort rests on a beautiful white$-$sand beach where guests can hear the gentle turquoise waves from their rooms. In the current market, the resort is priced around average compared to its closest competition. The general manager, Charles Gordon, believes that Serenity Hideaways offers more than competitors and is thinking about increasing the nightly room price from $$150$ to $$190$ in order to grow the resort's profits.

Serenity incurs certain variable costs each time it rents a room, including the costs associated with the labor and supplies necessary to clean and restock the room. However, the resort does not incur these costs if the room is not booked. Charles has determined that the resort's variable costs are $$45$ per room. Historically, Serenity Hideaways sells $6,000$ room nights per year, and over one year of operations, the resort incurs $$217,500$ in fixed costs. Answer the following questions based on Serenity's new proposed price point of $$190$ per night for a hotel room.

What is the contribution per unit $($room night$)$ for Serenity Hideaways?

What is the break$-$even point in number of room nights for Serenity Hideaways?

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What are the profits for Serenity Hideaways?

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What will the profits be if Serenity Hideaways sells $7,500$ units $($room nights$)?$

If a new competitor sets their price to $$80$ per night, should Serenity Hideaways match the price?

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