A metal factory produces metal bars for a customer who sets the specification of the length of the bars at 125 mm with a +/- 10% tolerance. The customer has set the quality standard of the delivery batch of the products that allows a maximum of 6% of defective products (i.e. the product's length falls outside the specification limits) to accept the whole batch delivered. The factory uses a processing machine to produce the metal bars with a capacity of 5,000 units produced within the 8 hours shift per day. The record of control chart shows that the machine's outputs have the average length of 129.5 mm with the standard deviation of 6 mm. The customer places a daily order of 5,000 units of metal bars, and the factory is determined to fulfil these orders consistently. The cost of material is $0.10 per mm. Based on the above information, answer the following questions: a. Calculate and provide your assessment on the capabilities index of the processing machine b. Calculate the percentage of defects that the machine will produce against the specification of the product. Can the factory's outputs that are produced within the normal shift meet the quality standard set by the customers? c. What possible solution(s) you can offer to the company to meet the quality standard set by the customer without changing the setting or condition of the machine? Show some calculations to support your solution and the implications of your solution d. If the factory can adjust the setting of the machine to change the average length of its outputs (without changing the standard deviation), determine the setting that the factory should choose to minimise the production cost for producing the metal bars but still meets the quality standard set by the customer. Show the calculations and explain your answers men