Boredom im Mathland

[cubby_t_bear]

Writing final exams is boring, so one has to amuse oneself somehow. The following was the best I could do:

Comments

[edgehopper]

Wait, do the elves simultaneously fire 8 arrows/min and decapitatte 0.5 orcs/min, or do they have to choose between the two (in which case they obviously specialize as archers and fighters)?

[chuckro]

Ooh, that's an important point. Assuming they're multitasking and both doing both, I think you need 120 elves/30 dwarves, but I cheated and just made a spreadsheet; there's obviously a more elegant answer.

[edgehopper]

I get 31 dwarves/119 elves (well, 30.97 dwarves, but dwarves are presumably quantized).

f=(1000-(8E+D))^2+(200-(E+2D))^2

Plug in E = 150-D, set df/dD = 0, note that because the D^2 term in f(D) is positive, that's a minimum.

[edgehopper]

And to a practical person with a computer, the spreadsheet is more efficient and therefore more elegant :) But my spreadsheet had a sum of squares of 6500 for 30 dwarves and 6451.25 for 31 dwarves.

[maydove]

I'm also writing a final exam. For tomorrow. (This week is crazy.)

[shnayder]

I like this question :)