Z'kXarmath (Employee assessment, Private Xarxos)

[Z'kron]

OOC: 1300th post celebration. *grins*
Opening the door to the inner office, the druid revealed a window-lit room with an arched ceiling and oaken furniture. Various diagrams of anatomy hung on the wall; and prominent on the ground was a large carved circle. Bookshelves lined two of the walls; while the other had a chalkboard on which various arcane diagrams were sketched. In the corner there was a box filled with soil, in which several reddish-colored spiney carrots were growing, the product of one of the druid's most recent experiments in Taralon. Completing the odd setup was a small basin of carved marble lying low to the ground in the centre of the room; similar to the type that one would expect would be used for scrying. Two well padded chairs sat comfortably near the basin.
"So, you're interested in mathematics, my friend. Tell me, what aspects of maths are you most interested in?"

[Xarxos Fineas]

OOC: lol. Congrats. =p 1,300 is a multiple of 5 =p

Walking in with 'Zkron, Xarxos entered the bizarre, though interesting, room. He looked around the room, and on seeing the small basin, he rushed over to wash his hands. While washing, he heard Z'kron mention "So, you're interested in mathematics, my friend. Tell me, what aspects of maths are you most interested in?"

"Well, I'm not quite sure. I can usually handle patterns of numbers really well but what I'd like to try is to find practical applications for mathematics. Not to waste money, time and effort. And tea. Must never waste tea. Tea is related to everything."

Xarxos dries his hands off and continues. " To find a practical use for maths, I must have a problem to solve. If you can give me a problem of a numerical nature such as business or mining, I'll try to solve it, and in doing so, find a practical application for maths."

Then, proceeding to look at the spiney, reddish-coloured carrots, Xarxos swayed back and forth slowly, while holding his hands.

[Z'kron]

"A numerical problem with a practical basis? Hmm. Well, it's hard to think of one off the top of my head that I couldn't simply do myself; advanced mathematics doesn't come up particularly often and I find arithmetic generally sufficient. Lets start simple then. Very simple."
The druid paused, dredging up a few modified examples from his earlier mathematical training in Arios, and his experience since then.
"Suppose I have a crop of carrots. I can grow 50 carrots per square geographical unit of this crop. My farm is 100 geographical units long and 80 geographical units wide. How many carrots can I produce?"

[Xarxos Fineas]

Turning towards the druid, Xarxos listens intently and strides over to the desk, looking for a pencil and paper.

On finding some, he scribbles vigorously at the paper only to stop and look at the druid questioningly. "The area of the farm is 8000 units in area and if you can grow 50 carrots square units, you can grow 400,000 carrots altogether. It's not exactly 50 carrots per square unit, is it though? Some areas may grow less then 50 because of say, bad soil conditions and others may grow more than 50. Would you be able to show me some records of the number of carrots you've grown in the past on such an area? I think I can make this prediction more accurate."

Xarxos then proceeds to write his results down neatly on the paper and presents it to Zkron.

On the sheet of paper:
Length of Farm = 100 units
Width of Farm = 80 units

Area of Farm = Length of Farm x Width of Farm
= 100 x 80
= 8000 square unit

Number of carrots per square unit = 50

Number of carrots grown on farm = 8000 x 50
= 400,000 carrots

[Z'kron]

"Very good! Of course, a more accurate record would be better. Give me a moment."
The druid moved to his desk, shuffling through a few papers. "How about something a lot more complicated?"
"Fresh market types are 3/4 to 1 1/4 carrot units in diameter (1 CU on average ; whereas processing carrots are large in diameter (2 to 3 CU, 2.5 CU average). Processing carrots usually produce 12 to 14 tons per geographical unit but can produce up to 30 tons per unit if put at optimal distance from other carrots. Fresh market carrots usually yield 8 to 12 tons per GU and can yield up to 20 tons at optimal distance from other carrots.
Fresh market carrots can be sold at a slightly higher price than processing carrots, depending on market fluctuations.

Each carrot requires twice its diameter of space around it in distance from the next carrot to grow reasonably. Assuming 1000 CU equals 1 Geographical unit, how much space would it take to grow 200 processing carrots as opposed to 200 fresh market carrots? Assuming you had 100 Geographical units, is it better to produce fresh market or processing carrots, if a fresh market carrot sells for 0.4 of a crown and a processing 0.3?"

[Xarxos Fineas]

Xarxos writes down Z'kron's question and starts drawing diagrams.

On the paper: http://static.flickr.com/118/299160478_0fbdb15e0f_o.jpg

"From what I can determine, we have the following pattern:

1 carrot requires 25 CU
2 carrots require 40 CU. An increase of 15 CU
3 carrots require 52.5 CU. An increase of 12.5 CU
4 carrots require 64 CU. An increase of 11.5 CU
5 carrots require 76.5 CU. An increase 12.5 CU
6 carrots require 88 CU. An increase of 11.5 CU

and so on and so forth.

Hence, 200 carrots of diameter 1 CU will require 2416 CU or 2.416 geographical units. "

He procceeds to scribble some more, grabbing more paper when he reached the end of the page:

Fresh Market types:
Minimum = 3/4 x 2.416 = 1.812 geographical units.
Average = 1 x 2.416 = 2.416 geographical units.
Maximum = 1 1/4 x 2.416 = 3.020 geographical units

Processing:
Minimum = 2 x 2.416 = 4.832 geographical units
Average = 2.5 x 2.416 = 6.040 geographical units
Maximum = 3 x 2.416 = 7.240 geographical units.

In 100 geographical units,

one could conceivably grow:

8332 carrots of diameter 1 CU. By reversing the above method for calculating units/carrot, we can work out carrots/ units. The above figure of 8332 carrots has been rounded down.

or

Fresh Market types:
Minimum = 8332/ 1 1/4 = 6665 carrots
Average = 8332/ 1 = 8332 carrots
Maximum = 8332/ 3/4 = 11,109 carrots

Processing:
Minimum = 8332/ 3 = 2777 carrots
Average = 8332/ 2.5 = 3332 carrots
Maximum = 8332/ 2 = 4166 carrots.

---- new page ----

This means that the revenue resulting from these carrots are:

Fresh Market types:
Minimum = 6665 x 0.4 = 2666 crowns
Average = 8332 x 0.4 = 3332 crowns 8 silver
Maximum = 11,109 x 0.4 = 4443 crowns 6 silver

Processing:
Minimum = 2777 x 0.3 = 833 crowns
Average = 3332 x 0.3 = 999 crowns 6 silver
Maximum = 4166 x 0.3 = 1249 crowns 8 silver.

The information regarding tonnes per GU of the two different carrots has been disregarded due to being irrelevant when the carrots are sold at price per carrot and not price per tonne.

We can see that Fresh Market types bring in more revenue than Processing carrots.

"Umm.. there's a problem. The revenue brought in by the Fresh Market carrots appear to be higher than the Processing carrots. However, I don't know what the costs of raising the two of them are, so I can't exactly which is more profitable."

[Z'kron]

The druid blinked once, then twice. He hadn't actually expected the applicant to complete the work sucessfully. In fact, he'd never really bothered to do the calcuations himself. And that the newcomer had managed in such a brief period of time was impressive in the extreme.
"Well. I think I'm going to dispense with any more formalities and hire you. You've displayed a rather adept grasp of mathematics, and a natural talent which surpasses mine by a massive amount. With the proper resources, you could do a great deal to help us. I'll employ you at, say, 100 crowns a cycle to be responsible for more mathematical advancement. And you can stay in quarters in the imperial forum for as long as you want. I'll also give you additional funding for any mathematical or any other type of advance you may acquire."
Z'kron gave a slight smile, just playing with an idea in his head.
"One more point. What is the logic by which that 0.999 recurring can by considered equal to 1?"

[Xarxos Fineas]

"And tea?" Xarxos asked, his eyes sparkling at the thought of free tea.

0.9 recurring equal to 1? Thinking about this for a moment, he let the idea swim around in his head. Cackling, Xarxos scribbled down some unintelligeble notes and procceeded to answer the druid. "If you multiply 0.9 recurring by 10, you would get 9.9 recurring. Then, if you took away 0.9 recurring from it, you would get 9. Let's try it with 1. If you multiply 1 by 10, you would get 10. Then, if you took away 1 from it, you would get 9. Using the same method with two numbers resulted in the same solution. Hence, the two numbers are equivalent, or 0.9 recurring is equal to 1."

"Hmmm... Is it possible for me to acquire my own library? I'd like to read to see what other tools and problems there are out there. Oh, and I'll need lots of paper and pencils. No pens."

[Z'kron]

"Yes yes, of course. As much tea as you want. Tea is no barrier where the empire is concerned."
Upon listening to the others solution - the new employee, as he now was- the druid gave a laugh of pleasure. "Quite right! Also true if you multiply by fractions. One third equalling 3.333 recurring, which multiplied by 3 is 0.9999 recurring; but which also equals one. Several neat little proofs there. We'll see about getting you a library to work in; I'm fairly certain we have somewhere devoted to mathematics where you can get to work. Consider yourself hired.... Xarxos, Imperial Researcher. Or Imperial Mathematician, if you choose that as your title. I'm not fussed. As long as you stay productive. I'll see if I can set up a locale in the forum for that. "
The druid smiled, jotting down a note of this employment on his desk.
"About time I had a look at what sort of facilities this place has to offer. To the library then, eh?"

[Xarxos Fineas]

"To the library!" exclaimed Xarxos, toasting his tea, and swigging it.