Problem
I. A coffee chain sells 441 different variations of beverages. It wants to maximize customer enjoyment of its hot coffee beverages. Its premium coffee blend tastes best at a temperature of 57.8 degrees C. Any cup of coffee that is at least 8.6 degrees below or above that value is discarded at a cost of $1.45.
What is the value of k in the loss function for this product?
II. A coffee chain wants to maximize customer enjoyment of its hot beverages. Its premium coffee blend tastes best at a temperature of 62 degrees C. If a cup of coffee is at least 7.2 degrees below or above that value, it is discarded at a cost of $0.85. The chain has 19,615 stores that together serve about 2.0 million cups per day.
If a particular cup of coffee is 59.0 degrees C, what is the loss it creates?
III. A pharmaceutical company manufactures pain relieving medicine. To provide maximum safe pain relief, each pill ideally should contain 199 g of the active ingredient; but any amount within +/- 16 g of that target is considered acceptable. Pills that fall outside of the specified range are destroyed, at a cost of $ 0.25 each. In a sample of 145 pills, the amount of active ingredient per pill actually had an average of 200.9 g and a standard deviation of 2.75 g.
What is the expected loss per pill?
IV. A coffee chain wants to maximize customer enjoyment of its hot beverages. Its premium coffee blend tastes best at a temperature of 58 degrees C. If a cup of coffee is at least 10.8 degrees below or above that value, it is discarded at a cost of $1.07.
One of the company's stores sells about 207 cups per day. The coffee there is actually served at a temperature that averages 58.3 degrees and has a standard deviation of 2.40 degrees.
What is the expected daily loss for this store?
V. A pharmaceutical company manufactures pain relieving medicine. To provide maximum safe pain relief, each pill ideally should contain 106 g of the active ingredient; but any amount within +/- 5 g of that target is considered acceptable. Pills that fall outside of the specified range are destroyed, at a cost of $0.58 each.
What is the value of k in the Taguchi (i.e., quadratic) loss function for this case?