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Sigmund Schwinn owns a popular bike shop called Cycle Analysts located in Ventura. Sigmund is participating in a bike show in San Francisco next month. At the show, he will have a special promotion on the Ninja Trail Master bike for $2,000 each. Estimated demand for this bike at the show is a normal distribution with a mean of 600 and a standard deviation of 20. Sigmund's cost is $1,000 per bike. Sigmund has already rented a large, one- way U-Haul truck to take the bikes to San Francisco. Each bike not sold at the show will be sold to a local bike vendor at a new loss of $200 to Sigmund. If Sigmund does not bring enough bikes to show, he will have to reduce the price to the customer by $200 and pay an additional $100 shipping to deliver the bike to the customer's residence using UPS next day delivery from Ventura. a. What is the probability that demand will be between 580 and 620 bikes? b. What is the probability that demand will be between 570 and 610? C. What is the unit cost of understock and the unit cost of excess (overstock) and the optimal percentile?

Sigmund Schwinn owns a popular bike shop called Cycle Analysts located in Ventura. Sigmund is participating in a bike show in San Francisco next month. At the show, he will have a special promotion on the Ninja Trail Master bike for $2,000 each. Estimated demand for this bike at the show is a normal distribution with a mean of 600 and a standard deviation of 20. Sigmund's cost is $1,000 per bike. Sigmund has already rented a large, one- way U-Haul truck to take the bikes to San Francisco. Each bike not sold at the show will be sold to a local bike vendor at a new loss of $200 to Sigmund. If Sigmund does not bring enough bikes to show, he will have to reduce the price to the customer by $200 and pay an additional $100 shipping to deliver the bike to the customer's residence using UPS next day delivery from Ventura. a. What is the probability that demand will be between 580 and 620 bikes? b. What is the probability that demand will be between 570 and 610? C. What is the unit cost of understock and the unit cost of excess (overstock) and the optimal percentile?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Sigmund Schwinn owns a popular bike shop called Cycle Analysts located in Ventura. Sigmund is participating in a bike show in San Francisco next month. At the show, he will have a special promotion on the Ninja Trail Master bike for $2,000 each. Estimated demand for this bike at the show is a normal distribution with a mean of 600 and a standard deviation of 20. Sigmund's cost is $1,000 per bike. Sigmund has already rented a large, one- way U-Haul truck to take the bikes to San Francisco. Each bike not sold at the show will be sold to a local bike vendor at a new loss of $200 to Sigmund. If Sigmund does not bring enough bikes to show, he will have to reduce the price to the customer by $200 and pay an additional $100 shipping to deliver the bike to the customer's residence using UPS next day delivery from Ventura. a. What is the probability that demand will be between 580 and 620 bikes? b. What is the probability that demand will be between 570 and 610? C. What is the unit cost of understock and the unit cost of excess (overstock) and the optimal percentile? d. Write the expression for the optimal number of bikes to pack in the U-Haul for the show.
Transcribed Image Text:Sigmund Schwinn owns a popular bike shop called Cycle Analysts located in Ventura. Sigmund is participating in a bike show in San Francisco next month. At the show, he will have a special promotion on the Ninja Trail Master bike for $2,000 each. Estimated demand for this bike at the show is a normal distribution with a mean of 600 and a standard deviation of 20. Sigmund's cost is $1,000 per bike. Sigmund has already rented a large, one- way U-Haul truck to take the bikes to San Francisco. Each bike not sold at the show will be sold to a local bike vendor at a new loss of $200 to Sigmund. If Sigmund does not bring enough bikes to show, he will have to reduce the price to the customer by $200 and pay an additional $100 shipping to deliver the bike to the customer's residence using UPS next day delivery from Ventura. a. What is the probability that demand will be between 580 and 620 bikes? b. What is the probability that demand will be between 570 and 610? C. What is the unit cost of understock and the unit cost of excess (overstock) and the optimal percentile? d. Write the expression for the optimal number of bikes to pack in the U-Haul for the show.
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