Question

Bratt's Bed and Breakfast, in a small historic New England town, must decide how to subdivide (remodel) the large old home that will become their inn. There are three alternatives: Option A would modernize all baths and combine rooms, leaving the inn with four suites, each suitable for two to four adults. Option B would modernize only the second floor; the results would be six suites, four for two to four adults, and two for two adults only. Option C (the status quo option) leaves all walls intact. In this case, there are eight rooms available, but only two are suitable for four adults, and four rooms will not have private baths. Below are the details of profit and demand patterns that will accompany each option. Which option has the highest expected value?Annual profit under various demand patterns Capacity p Average pA (Modernize all) $90,000 .5 $25,000 .5B (Modernize 2nd) $80,000 .4 $70,000 .6C (Status Quo) $60,000 .3 $55,000 .7

Answer 1

Answer:

Option B (Modernize 2nd) has the highest expected value which $74,000.

Explanation:

Note: The data in the question are merged together. They are therefore sorted before anwering the question as follows:

                                  Annual profit under various demand patterns

                                    Capacity          p           Average             p

A (Modernize all)         $90,000         .5          $25,000            .5

B (Modernize 2nd)      $80,000         .4          $70,000             .6

C (Status Quo)             $60,000         .3          $55,000             .7

The explanation to the answer is now provided as follows:

The expected value is estimated as the addition of the multiplication of each possible outcomes by the probability of occurrence of each outcome.

The expected value for each of the options in the question can therefore be estimated using the following formula:

Expected value = (Capacity * p of Capacity) + (Average * p of Average)

This formula is therefore applied to each options as follows:

Option A expected value = ($90,000 * 0.5) + ($25,000 * 0.5) = $45,000 + $12,500 = $57,500

Option B expected value = ($80,000 * 0.4) + ($70,000 * 0.6) = $32,000 + $42,000 = $74,000

Option C expected value = ($60,000 * 0.3) + ($55,000 * 0.7) = $18,000 + $38,500 = $56,500

Based on the calculations above, Option B (Modernize 2nd) has the highest expected value which $74,000.