The Greatyear Tire Company has developed a new tire and wants to jump start the marketing of this tire.Based on their testing of the product, it has mean lifetime of 36,500 miles and a standard deviation of 5,000 miles.They also determined that the lifetime follows a normal distribution with those parameters quite well.

The marketing department decided on the following plan for promotion of the product:they are so sure that the product will wear well that they will promise to pay a rebate for any tire that needs replacement at a threshold.They are considering 5 thresholds:28,000, 29,000, 30,000, 31,000 and 32,000 miles, respectively.They will pay the purchaser back $1 for each full 100 miles the tire is below this threshold.(For example, if the threshold is 29,000, and the tire is replaced at 27,430 miles, the below threshold mileage is 1,570 miles (= 29,000-27,430).Then, the below threshold mileage is divided by 100 (that yields 15.7), so the number of FULL 100s below is 15.This person would be paid $15 for that tire.)

• A) Determine the input variables of this problem:
  • What is(are) the input random variable(s)?
  • What is(are) the decision variable(s)?
• B) Set up a simulation model in @Risk for each of the 5 different thresholds.Use 1000 replications for each alternative threshold.Also, show the Mean, Standard Deviation, Max rebate, and the probability that a rebate will exceed $5. Copy and paste your table. Discuss the results briefly (2-3 lines).
• HINTS:
  • Use the spreadsheet titled IA5_Q2_Tire_templatet.xlsx as a starting point for this analysis.
  • The sections shaded in yellow are intended to assist you organize the information.
  • Add the simulation functionality to the template to output the rebate per tire (add randomness to any random variables and designate the appropriate outputs).
  • To round the number FULL 100s down to the nearest integer, use ‘INT’ function in Excel.
  • Use RiskSimTable to compute the summary statistics for all five thresholds simultaneously. Management expects that the promotion will run for the initial 3 months after release and that sales will be approximately 2 million tires in that period.However, they do not want to invest more than $5 million in the rebate program.
• C) Based on the simulation results, compute the mean total cost for each alternative threshold assuming that sales will be 2 million tires.
• D) Based on the results in part (c), what threshold level would you recommend that Greatyear use so that they will have strong sales but not exceed the $5 million limit in rebate cost. Explain your answer. At that level, what percent of tires will see a greater than $5 rebate?