Four Lines, Not Fifteen: Sizing a Can Plant on the Right Calendar
Twelve million people at six cans a week is 3.744 billion cans a year, which over the 525,600 minutes a calendar year offers is 7,123 cans a minute, or 3.56 production lines, or 4.19 once 85 percent uptime is allowed. Size the same demand on a 40-hour week and you get exactly 15 lines, because the two calendars differ by 219/52 = 4.2115, a systematic factor that no numerator guess can cancel. Sweeping all four inputs over 200,000 draws moves the count between 1.4 and 7.7 with a median of 3.4, so the conclusion is sturdier than any of the guesses inside it.