Scenario 16.1 - The Stone Lion
The Stone Lion,a bed and breakfast located in a sleepy town,caters to two groups of customers,young couples interested in something marginally more exotic than a staycation,and corporate clients interested in doing some team-building at a location with no cellular service.Corporations know they can get rooms with minimal notice,but young couples on tight budgets tend to plan well in advance of their planned stay at the property.The corporate rate for rooms is $250 per person and the demand pattern is normal with a mean of 20 and a standard deviation of 10.The proprietor of the Stone Lion takes pity on the young couples and charges them only $150 for identical accommodations.
-If the price young couples are willing to pay increases by 50%,how many rooms should be reserved for corporate clients?

Question

Quizplus · Accepted Answer

First, we need to calculate the new price that the young couples are willing to pay, which is $225 ($150 x 1.5). 
Next, we need to determine the point at which the revenue from the young couples equals the revenue from the corporate clients. 
To do this, we can use the formula for normal distribution: z = (x - μ) / σ, where z is the z-score, x is the value we are interested in (in this case, the number of rooms reserved for corporate clients), μ is the mean, and σ is the standard deviation. 
We want to find the z-score where the area to the right of it is 0.5 (since we want to find the point where the revenue from the young couples equals the revenue from the corporate clients). Using a standard normal distribution table, we find that the z-score is 0. 
So, we can set up the equation: 
250(20-x) = 225x 
Solving for x, we get x = 7. 
Therefore, we should reserve 7 rooms for corporate clients.

Scenario 16.1 - the Stone Lion