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.
