Question 6: Quality Control (Bonus Question: 5 pts. Warning: Very challenging!) Due to liability issues it is imperative that drug makers have rigorous quality-control standards. Production control at Betapharm requires that its Malic acid input have a pH level between 2.9 and 3.1, and the size of each particle of Malic acid be between 7 and 10 microns. Any substance with attributes falling beyond either the pH or size tolerances would be considered defective. Betapharm required that its suppliers have a defect rate of no more than 2x10-9. Marina' s report indicates that Chun Wu planned to use a two-step serial process: (A) Malic acid pH titration; and (B) Malic acid grinding. Chun Wu' s step (A) is carried out in a reactor which sets the acid pH to a mean of 3.0 with a standard deviation of 0.016 pH. Step (B) grinds material to a mean of 8.5 microns with a standard deviation of 0.27 microns. Being an experienced six sigma black belt, Marina estimates that improving step (A) would require building new reactor (millions of dollars) and is financially infeasible. However, capability improvement at step (B) is possible, and it would require costs directly proportional to the amount of improvement. She estimated that reducing step (B)' s standard deviation by a factor of x% would cost (E200,000)(x%) annually in calibration and sampling expenses; for example, reducing standard deviation by 50% would cost E100,000 per year. Estimate how much it will cost annually to bring Chun Wu up to Betapharm' s required quality level. (Hint: You will need to use the following relation: Prob (meet specs) = Prob (meet specs in A) * Prob (meet specs in B).)