Roger Hunt intends to purchase one of two car dealerships currently for sale in a certain city. Records obtained from each of the two dealers reveal that their weekly volume of sales, with corresponding probabilities, are as follows. Dahl Motors Farthington Auto Sales The average profit/car at Dahl Motors is $367, and the average profit/car at Farthington Auto Sales is $439.
If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase? (Compare the expected weekly profit for each dealership.)
A) Farthington Auto Sales
B) Dahl Motors
C) either of the two

Question

Roger Hunt intends to purchase one of two car dealerships currently for sale in a certain city. Records obtained from each of the two dealers reveal that their weekly volume of sales, with corresponding probabilities, are as follows. Dahl Motors   Farthington Auto Sales  The average profit/car at Dahl Motors is $367, and the average profit/car at Farthington Auto Sales is $439.
If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase? (Compare the expected weekly profit for each dealership.)
A) Farthington Auto Sales 
B) Dahl Motors 
C) either of the two

Quizplus · Accepted Answer

To find the expected weekly profit for each dealership, we need to multiply the average profit per car by the probability of each level of sales, and then sum those products.

For Dahl Motors:
Expected weekly profit = (0.2*$367*20) + (0.4*$367*25) + (0.4*$367*30) = $8,762

For Farthington Auto Sales:
Expected weekly profit = (0.1*$439*15) + (0.2*$439*20) + (0.4*$439*25) + (0.2*$439*30) + (0.1*$439*35) = $10,155

Therefore, Roger should purchase Farthington Auto Sales since it generates a higher expected weekly profit.

Roger Hunt Intends to Purchase One of Two Car Dealerships