The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule?
A) $187,000
B) $132,000
C) $123,000
D) $65,000
E) $55,000

Question

The construction manager for ABC Construction must decide whether to build single family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows:

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule?

What is the expected annual profit for the dwellings that he will decide to build using Bayes' decision rule?
A) $187,000 
B) $132,000 
C) $123,000 
D) $65,000 
E) $55,000

Quizplus · Accepted Answer

Using Bayes' decision rule, we need to calculate the expected annual profit for each type of dwelling and choose the one with the highest expected profit.

Expected profit for single family homes:

($200 * 0.2) + ($60 * 0.3) + ($20 * 0.5) = $68,000

Expected profit for apartments:

($400 * 0.2) + ($200 * 0.3) + ($50 * 0.5) = $130,000

Expected profit for condominiums:

($300 * 0.2) + ($120 * 0.3) + ($80 * 0.5) = $97,000

Based on these calculations, the best choice would be to build apartments, which have the highest expected profit of $130,000. Therefore, the answer is B.

The Construction Manager for ABC Construction Must Decide Whether to Build