MarshaRae
Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Jim decides to start a small nonprofit business of renting out motor scooters to help out his area residents. He puts in his own money and buys 5 motor scooters, each priced at $3,000. He incurs no other costs because he keeps the motor scooters in his own garage. The motor scooters last for 5 years. The number of motor scooters and the probability that they would be rented per month is shown in the table.

Number of Scooters 0         1          2           3            4       5
Probability              1/32     5/32     10/32     10/32     5/32    1/32


At what price per month should Jim rent out a scooter in order to break even?

A) 50
B)150
C)200
D)250
E)300

Sagot :

ollieboyne
First, find the expected number of scooters rented per month:

As the data is symmetrical, E(X) (the expected value) is the middle value. So, on average, 2.5 scooters should be taken per month.

His total costs were 5 * 3000 = $15,000

So, to break even, he needs to make $15,000.

He will be selling for 5 years, or 60 months.

As a result, he needs to make 15000/60 = $250/month

As he is selling 2.5 scooters on average, he needs to rent each for:

$250/2.5 = $100/month
kate200468
[tex]the\ expected\ value:\ \ \ E[X] = x_1p_1 + x_2p_2 + \dotsb + x_kp_k \\\\ E[X] =0\cdot \frac{1}{32} +1\cdot \frac{5}{32} +2\cdot \frac{10}{32} +3\cdot \frac{10}{32}+4\cdot \frac{5}{32}+5\cdot \frac{1}{32}= \frac{80}{32} =2.5\\\\5\ motor\ scooters\ \ \rightarrow\ \ \ 5\cdot \$3.000=\$15.000\\\\5\ years=5\cdot 12\ months=60\ months\\\\2.5\ motors\ monthly\ \ \rightarrow\ \ 2.5\cdot60=150\ motors\ at\ 5\ years\\\\[/tex]

[tex]x\ \ \rightarrow\ \ the\ price\ per\ month\ (to\ break\ even)\\\\150\cdot x=\$15.000\ \ \ \Rightarrow\ \ \ x= \$100\\\\Ans.\ \ \$100[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.