solution

g 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 net loss of $100 to Sigmund. If Sigmund does not bring enough bikes to the show, he will have to reduce the price to the customer by $250 and pay an additional $150 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 560 and 640 bikes?

b. What is the probability that demand will be between 590 and 630?

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.