The Stanley Hotel is regarded as one of the spookiest hotels in the U.S. and was the inspiration behind Stephen King's Novel, The Shining. Because of this, it has become a hotspot for tourists and has ample demand at its low-fare price of $329/night. The hotel has a high-fare price for those who book a stay last minute, at $349/night. The hotel finds the last-minute booking requests occur with a normal distribution with a mean of 20 and a standard deviation of 7.

The hotel has a total of 140 rooms that can be booked. The Hotel completed an expense analysis and found that for every occupied room, they incur a cost of $150 in labor expenses, wear and tear, additional utilities used, etc. (This cost does not depend on whether the room is being used by high or low-fare customers and is only incurred when the room is occupied.)

What should the new protection level be for high-fare customers to maximize profits factoring in this new information?