Questions: Jasmine Dantas' Bed and Breakfast, in a small historic Mississippi town, must decide how to subdivide (remodel) the large old home that will become its status quo option) leaves all walls intact. In this case, there are eight rooms available, but only two are suitable for four adults, and forty. Option C (the have private baths. Below are the details of profit and demand patterns that will accompany each option: Alternatives Annual Profit under Various Demand Patterns ------ High p Average p A(modernize all) 96,000 0.50 27,000 0.50 B (modernize 2nd) 84,000 0.30 70,000 0.70 C (status quo) 64,000 0.25 50,000 0.75 This exercise contains only part b. b) The option with the highest expected value for Jasmine Dantas' Bed and Breakfast is . with an expected value of 5 round your response t the nearest whole number).

Solution Steps

The expected value for Option A is calculated as follows:

\[ \text{Mean} = 96000 \times 0.5 + 27000 \times 0.5 = 61500.0 \]

The variance for Option A is calculated using the formula:

\[ \text{Variance} = \sigma^2 = (96000 - 61500.0)^2 \times 0.5 + (27000 - 61500.0)^2 \times 0.5 = 1190250000.0 \]

The standard deviation is then:

\[ \text{Standard Deviation} = \sigma = \sqrt{1190250000.0} = 34500.0 \]

The expected value for Option B is calculated as follows:

\[ \text{Mean} = 84000 \times 0.3 + 70000 \times 0.7 = 74200.0 \]

The variance for Option B is calculated using the formula:

\[ \text{Variance} = \sigma^2 = (84000 - 74200.0)^2 \times 0.3 + (70000 - 74200.0)^2 \times 0.7 = 41160000.0 \]

The standard deviation is then:

\[ \text{Standard Deviation} = \sigma = \sqrt{41160000.0} \approx 6416.0 \]

The expected value for Option C is calculated as follows:

\[ \text{Mean} = 64000 \times 0.25 + 50000 \times 0.75 = 53500.0 \]

The variance for Option C is calculated using the formula:

\[ \text{Variance} = \sigma^2 = (64000 - 53500.0)^2 \times 0.25 + (50000 - 53500.0)^2 \times 0.75 = 36750000.0 \]

The standard deviation is then:

\[ \text{Standard Deviation} = \sigma = \sqrt{36750000.0} \approx 6062.0 \]

The expected values for each option are as follows:

• Expected value for Option A: \( 61500.0 \)
• Expected value for Option B: \( 74200.0 \)
• Expected value for Option C: \( 53500.0 \)

The option with the highest expected value is Option B with an expected value of \( 74200.0 \).

Final Answer