In an assembly process, its current quality level is considered to be at a 3-process with a 1.5-mean- shift (i.e., =T+1.5). To produce each product, the manufacturing cost is $20. Some initially rejected defective products can be manually adjusted or reworked to make them saleable at full price. Assuming a reworkable rate of 60% for those initial rejections, with an additional cost of $4 per reworkable part. If the company adds an automatic smart calibration device (ASC), it is expected that the process will be improved to be a 3-centered-process (i.e., =T). The company needs to evaluate the profit for their business decision whether to install an ASC device. Assuming the total production volume is 100,000 products this year and the sale price of each good product is $30/product. (Assume the reworkable rate is the same before and after installing an ASC device, and the production volume and product's sale price will not change for the next year.) To make the decision, the company wants to compare the next year's profit before and after adding this ASC device. For this purpose, you may help to answer the following questions: (a) What is Cpk for the process before and after adding an ASC device? What is the defective rate (ppm) of the process before and after installing such an ASC device? (b) What is the total manufacturing cost (C) by considering the rework cost before and after installing an ASC device? (c) What is the total number of salable good products (S) by including the reworkable products before and after installing an ASC device? (d) What is the total profit (P) before and after installing an ASC device? How much extra profit (T) can be generated in the next year if the company decides to install an ASC device? If the ASC device costs $40,000, will you recommend installing this ASC device