A quality control engineer knows that his product quality, X, is normally distributed with mean 10 and standard deviation 2 under the current production procedure with cost per unit produced equal to 1$. If he increases the quality by reducing the process standard deviation to 1, his cost per unit will double. He can sell the products only if the quality is more than 2 otherwise the product is trashed. Is it really beneficial for him to reduce the standard deviation with the extra cost that it brings?