12. An automatic cookie machine at ACM, Inc. must deposit a specified amount of 25 ` 0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a defective cookie. A sample of 50 cookies was drawn from the production process, which has been determined to be approximately normally distributed, and the results, in grams, can be found in worksheet tab Prob. 7-12 in the Excel file C07Data. a. What is the value of k in the Taguchi loss function? b. Determine how much the process varies from the target specification, based on the mean difference and standard deviation of the sample results. What is the expected loss per unit? 15. At Elproparts Manufacturers' integrated circuit business, managers gathered data from a customer focus group and found that any output voltage that exceeds 60 ` 3.5 volts was unacceptable to the customer. Exceeding these limits results in an estimated loss of $90. However, the manufacturer can still adjust the voltage in the plant using a quick diagnostic test that costs $3.75. a. Determine the Taguchi loss function. b. Suppose the nominal specification remains at 60 volts. At what tolerance should the integrated circuit be manufactured? 29. CajaGigante, a large department store, has a very successful and profitable package-wrapping department. The department uses two complex bow- making machines that work inline to make the bows for the packages. There is one skilled operator who knows how to operate the machines. She had been very reliable, but recently has had increasing health problems which caused her to miss work about 10 percent of the time. Bow-making Machine 1 has a reliability of 0.97. Machine 2 has a reliability of 0.90. a. What is the current reliability of the system, including the operator? b. Management is considering either scrapping Machine 2 and replacing it with a new machine which has a reliability of 0.97 at a cost of $5,000, or training another operator to fill in when the first operator is absent at a cost of $5,100. The prospective trainee has an excellent attendance record and has only been absent 4 days out of 250 work days for the department, last year. Management estimates that profits from the department would increase by $6,000 per year, if the bow- making line operated at 100 percent of capacity. If management wants to pay off its investment in the first year, determine the expected net profit for each alternative, and recommend which one will be the most profitable to management.