Question: A critical electronic component with mean time to failure of x years can be purchased for 2x thousand dollars (thus, the more reliable the component, the more expensive it is). The value of x is restricted to being between 1 to 10 years, and lhe actual time to failure is modeled as exponentially distributed. The mission for which the component is to be used lasts one year; if the component fails in less than one year, then there is a cost of $20,000 for early failure. What value of x should be chosen to minimize the expected total cost (purchase plus early failure)? To solve this problem, develop a simulation that generates a total cost for a component with mean time to failure of x years. This requires sampling an exponentially distributed random variable with mean x, and then computing the total cost as 2000x plus 20,000 if the failure time is less than I. Fit a quadratic meta model in x and use it to find the value of x that minimizes the fitted model. [Hints: Select several values of x between 1 and 10 as design points. At each value of x, let the response variable Y(x) be the average of at least 30 observations of total cost.]