Problem: Knoop Inc. (25 points) COVID-19 has had an impact on all aspects of our lives. Perhaps one positive aspect is that people are becoming more health-conscious and a healthy lifestyle is becoming popular. A French company Knoop Inc. has purchased the piece of land in Little Rock and is planning to set up a bicycle assembly unit there. These new bikes will be built in a modern plant and the management believes the bikes will be very popular. The assembly plant and technology will be provided by a Danish company. Knoop is very optimistic about the performance and sales potential of these bikes in AR and other southern states. They believe their new models will last for at least 200,000 miles without any breakdowns. However, an independent research company has conducted extensive tests and their report shows an average life of 120,000 miles. Knoop thinks they should give a guarantee of 120,000 miles while their consultants are recommending 90,000 miles. You have recently been hired by Knoop Inc. as the marketing manager and are assigned to the project. 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 120,000 miles and a standard deviation of 12,500 miles. You quickly figure out that a guarantee of 120,000 miles might become a disaster for the firm. You mention this issue to your boss but she is too busy (and of course dumb) to give it a serious thought. Instead, she asks you to submit a report with your analysis and recommendations.

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

a. Is 120,000 miles guarantee a good idea? Why or Why not? Quantify your answer (submit your calculations) What about 90,000 miles? (5 points)

b. If they decide to go for 90,000 miles, What percentage of bikes will meet this minimum criteria? What percentage will not meet the criteria? (5 points)

c. 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)

d. 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)

e. Write a memo to Ron and Tom, presenting your findings, conclusions, and recommendations. (5 points)