Question
Pete owns a small business renting out bicycles in Vancouver. He rents each bike for $5 a day. After a year, his rental bikes are
Pete owns a small business renting out bicycles in Vancouver. He rents each bike for $5 a day. After a year, his rental bikes are worn out and basically worthless. So each year Pete gives his old bikes to a local charity and replaces his entire fleet of bikes. Pete buys his bikes from a local manufacturer at the discounted price of $500 each. Pete has estimated the following probability distribution of the number of bikes he can expect to rent on any given day:
Number of bikes rented per day | 10 | 11 | 12 | 13 | 14 |
Probability | 0.10 | 0.25 | 0.40 | 0.20 | 0.05 |
After Pete rents out a bike, he has to clean and tune it before he can rent it out again. The average cost of this maintenance is $2 per bike. This includes the cost of materials and the opportunity cost of Petes time. Petes store is open five days a week year-round, except during a four-week period each January when he goes skiing. How many bikes should Pete buy each year to maximize his expected profit?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started