It’s a cold, hearty Canadian morning and you need a coffee. So you saunter over to the coolest hipster coffee-shop in town, OR Café, and plop yourself down on one of the massively comfy couches. You barely get yourself comfortable when you feel a soft tap on your shoulder. Turning, you see Curtiss and Shefali, the friendly store managers. You smile at them, but you quickly realize that all is not well.
“It’s the penny!” Curtiss exclaims grimly, “They’re taking it away!” You think back to this week’s news while he continues, “Call me Canadian, but I can’t stand the idea of rounding prices up for my customers! It’s terrible! I’ve been up all night trying to find new prices that round nicely, but I can’t figure out how! It’s really quite difficult…” Thinking about your coffee, you realize that the $1.24 you paid for it plus the 13% Ontario sales tax comes out to exactly $1.40. However, had you purchased a donut with your coffee, the final price would be $2.47. And apparently that’s somehow unacceptable.
Curtiss rambles on, “Your mission, should you choose to accept it, is to determine the menu that minimizes the number of times that we have to round a customer’s purchase, up or down. Of course, we don’t want to change prices by too much, so you may only move prices up or down by up to 2 cents.” Shefali, surprisingly silent up to now, slides over a USB key and says, “ We’ve been keeping track of customer purchases; here is what people have been buying. I hear you’re good at this operations research stuff, so you know how to use this, right?” You sigh, roll your eyes, pull out a pen and paper and start jotting down some ideas. As crazy as these people are, they definitely come up with some interesting questions…