There is a story (perhaps it is just an urban legend) that in the the 1960s a toothpaste manufacturer faced a financial crisis. They were desperate to make the sales go up, but nothing seemed to work. Finally, a guy came by and offered to increase their sales by at least 50% in exchange for $100,000. At first the company declined the proposal on account of being to expensive and coming from a person with no track record. However, after a year the management saw no other option, but to accept the offer. After all the legal details were set, the guy spoke only one sentence: “Make the hole bigger”.
Note: $100,000 may not sound like a tone of money today, but if you update it for an inflation rate of let’s say 3.6% you will get roughly $1,000,000. Example calculations: 100,000*(1.036^65) \(\approx\) 996,000,000. In that case 65 is the number of years between 1960 and 2025, whereas 1.036 is how much more money you must spend every year on the same product due to the assumed inflation). We will deal with similar calculations in Section 13.
Try to figure out does making the hole bigger actually moves the sales up by \(\geq\) 50%. Test different scenarios, e.g. different initial hole size, and see what would have happened if the customers tried to counteract this idea by squeezing less toothpaste (shorter strip) on the toothbrush.