Problem: Pawnee Bikes (35 points)

Leslie Knope has been elected as the Mayor of Pawnee. She is very excited about it as she will be able to fulfill her dream of setting up a new park at the abandoned construction site. However, her dream is shattered when she comes to know that Ron Swanson and Tom Haverford have purchased the piece of land and are planning to set up a bicycle assembly unit there. They believe the new bicycles will be very popular as these will be manufactured from carbon fibers and will last much longer than any other bicycle available. The assembly plant and technology will be provided by a Danish company. Ron is very optimistic about the performance and sales potential of these bikes. He believes the bicycles will last for at least a million miles without any breakdowns. However, an independent research company has conducted extensive tests and their report shows an average life of 87,900 miles. Tom thinks they should give a guarantee of 120,000 miles while Ron is more inclined to go for 76,000 miles. You have recently been hired by Ron as an assistant manager and are assigned to the marketing team. While going through the test results you notice that the analysis mentions a large number of tests that were conducted and that the test data followed a normal distribution with a mean of 87,900 miles and a standard deviation of 2,050 miles. You quickly figure out that a guarantee of 120,000 miles might become a disaster for the firm. You mention this issue to Tom but he is too busy (and of course dumb) to give it a serious thought. Instead, he asks you to submit a report with your recommendations.

Conduct an analysis of this problem that should address (at least) the following:

1. Is 120,000 miles guarantee a good idea? Why or Why not? Quantify your answer (submit your calculations) What about 76,000 miles? (15 points)
2. If they decide to go for 76,000 miles, What percentage of bikes will meet this minimum criteria? What percentage will not meet the criteria? (5 points)
3. Assume that if a bike does not meet the minimum mileage warranty it will have to be replaced. What should be the claimed mileage if you want no more than 5% of the bikes to be replaced? (5 points)
4. Ron plans to sell 50,000 bikes in the first year. Suppose he sets the minimum mileage to your solution in part (c) above and each bike replaced will cost $500. Further assume that not all customers whose bikes breakdown sooner than the guarantee period will make a claim. In fact historical data shows probability of such customers making a claim for replacement is only 0.35. If that is true then what is the expected cost of bikes replacement (assume a sold volume of 50,000 for this calculation)? (5 points)
5. What type of memo would you give to Ron and Tom, presenting your findings, conclusions, and rec- ommendations. (5 points)