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 Cars Sold/Week 5 6 7 8 9 10 11 12 Probability 0.05 0.09 0.14 0.24 0.18 0.14 0.11 0.05 Farthington Auto Sales Cars Sold/Week 5 6 7 8 9 10 Probability 0.08 0.21 0.31 0.24 0.10 0.06 The average profit per car at Dahl Motors is $544, and the average profit per car at Farthington Auto Sales is $651.

(a) Find the average number of cars sold each week at each dealership. Dahl cars Farthington cars
(b) If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase

Answer 1

(a) Dahl Motors = 8 Cars

Farthington Auto Sales = 7 Cars

(b) Roger will purchase from Farthington Auto Sales with higher weekly profit

Explanation:

Dahl Motors / Week

(1) Car Sold 5 6 7 8 9 10 11 12

(2) Probability 5% 9% 14% 24% 18% 14% 11% 5%

(3) (2 x 3 ) 0.25 0.54 0.98 1.92 1.62 1.40 1.21 0.60

(4) Average sales = 0.25 + 0.54 + 0.98 + 1.92 + 1.62 + 1.40 + 1.21+0.60

= 8.52‬ cars/ week

= 8 cars /week

Profit/ Car = $544

Total weekly profit = 544 x 8

= $4,352

Farthington Auto Sales/ Week

(1) Car Sold 5 6 7 8 9 10

(2) Probability 8% 21% 31% 24% 10% 6%

(3) (2 x 3 ) 0.40 1.26 2.17 1.92 0.9 0.6

(4) Average sales = 0.40 + 1.26 + 2.17 + 1.92 + 0.90 + 0.60

= 7.25‬ cars/ week

= 7 cars/week

Profit/ Car = $651

Total weekly profit = 651 x 7

= $4,557‬

From the calculations above , Roger will purchase from Farthington Auto Sales