Operation Management: Please right what's the Objectives and Formula

1. Linda Boardman, Inc., an equipment manufacturer in Boston, has submitted a sample cutoff valve to improve your manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean (m) of 8.00 and a standard deviation (s) of .04. Your desired performance is m = 8.0 {3s, where s = .045. What is the Cpk of the Boardman valve? 2. As the supervisor in charge of shipping and receiving, you need to determine the average outgoing quality in a plant where the known incoming lots from your assembly line have an average defective rate of 3%. Your plan is to sample 80 units of every 1,000 in a lot. The number of defects in the sample is not to exceed 3. Such a plan provides you with a probability of acceptance of each lot of .79 (79%). What is your average outgoing quality? 3. Dale the farmer and his brother Jake decide to sell the family farm. They will use the proceeds to invest in the stock market. As they cannot agree on an investment choice, they split their money. Dale wants to buy stock "Bull" with his half million "Bull" currently sells for $46 per share. What is Dale's return if he buys on margin as much stock as he can. His broker requires a 50% initial margin and he charges a 2% annual fee on the loan amount. If Dale invests all that he can, what is Dale's return if the stock price after one year is 51 dollars per share? Please write your answer in decimal format (please write 21.2% as .212, please write negative numbers with a - symbol before them) and do not use $ or % in the answer. Please use 5 decimal places in your response