Hitchcocks Forum

Hi guys------- Please bear with me on this and read through to the end}-----Just been having an interesting discussion about the need for accuracy when calculating growth....I think most of you will know the old story about a Chinese worker asking for his wages to be doubled every month, starting with an initial payment of 1 grain of rice ??......How many grains of rice will he have in total at the end of a year ??............Apparently this is called Exponential Growth or Expantion but is there a mathematical formula to work out the answers ???............


."What has this to do with my faithfull Bullet?" you might ask......OK, take the new twin that's about to be launched and let's suppose that the MD at Enfield HQ in a moment of sheer optimism commits the factory to doubling the output month-on-month for the first year, starting with just one machine..... Well, the materials procurement department will want to know well in advance so that they can match the arrival of steel, Aluminium, plastics, sub-contracted items, etc to the flow of the production line, which in itself will have to be jacked-up each month to cope.......... The Personnel Department will be having a logistics nightmare of their own where at the outset there was enough people to produce one unit ( Bike ) in a month----- but by the end of the year may well have seen the entire workforce doubled and gone onto 24 Hr , 7 day week working in order to cope !!..............Then there's the storage and delivery, sales etc.. etc....And don't forget the Corporate Tax to be paid based on output and / or sales and from that comes the half-yearly returns for the investors information......So, is there some sort of mathematical equation such that the figures can be calculated for any one particular time in the year ahead ???.............................Incidentally, doing it the hard way, month 6 sees 32 bikes produced with a rolling total of}----- 63 produced whilst month 12 sees 2,048 in that month with a grand total of}----4,095 bikes total in the first year.

I can`t help you there, I can`t work out the grocery bill every month; however, there is form to the equation used by factories called JIT (just in time) used from the 1960`s as far as I know by the Hobart Food Corporation where I used to work, and many other firms. Parts were manufactured and machines built using this system. Now can anyone help me with my shopping list?

Let the first month be month 0 (zero)

Then the number of bikes in month n is 2ⁿ (2 x 2 x ... n times)

So in the sixth month you produce 2⁵=32 bikes.
In the twelfth month you produce 2¹¹ = 2048
And by the last month of the second year, 8,388,608 bikes per month.

And the total number of bikes produced is 2ⁿ⁺¹ - 1, so at the end of 2 years you will have made 16,777,215 bikes.

And after about 11½ years you are producing more bikes per month than the number of atoms in the universe.

I’d use a spreadsheet, allowing graphical as well as numerical output via the graph function. That way you could read each month’s expected production at a glance.

Or as a bar chart.

Hi guys---------and thanks for entering into the spirit of the question.....and particularly to ed lazda for providing the formula.....Based on your last comment, let's hoe that Enfield don't plan to bring out a 750cc Atom Twin motorcycle....With that projection of yours we'll all end up on the production line....LoL !!.............. ......
Hi Leon}----Yes, at the MoD Workshops here in Telford they also used the JIT approach, but if I arrived at 07.59 and was supposed to be dismantling a tank at 08.00 they got quite upset !!!...Just no pleasing some folk, eh ??
The conversation I referred to at the beginning of the thread was how well-meaning ideas that have not been thought through could have unintentional and potentially disastrous consequences..........

Here's another one..Not actually true, but you get the idea}--- During WW2 and after the RAF and the American 8th Army Air Force had started their 1,000 plane,heavy bombing campaigns, someone at London H/Q thought it a good that ALL planes must be able to start-up each time......So they issued an order that before the next offensive took place ALL planes must have their old spark plugs changed for new........Here are the numbers, you work it out}----- Flying Fortress = 4 engines with 9x2 cylinders per engine...............Lancaster = 4 engines with 12 cylinders per engine...........Assume both types used two plugs per cylinder....and 1,000 planes per mission....( OK, not strictly true I know but other makes might well have a similar set-up )............How many plugs will KLG, Champion etc have to supply by next week ??

Sorry Rattlebattle---I was just typing my reply when you answered..........Yes, that would do it quite nicely I think.....Have a go at the next one if you like.....Answers on a postcard please !!--LoL !!

My brain hurts!