
Word Problem
Trying to figure this out for a game I am playing. Thought It might be fun for someone and it would sure be helpful to me :) I will put it in the form of a word problem.
A space travelling merchant finds a bargain on a particular ore. He purchases 500 Units of this ore for 85 space bucks per unit. This particular ore when refined breaks down into three different minerals. 500 units of this ore yield 321 units of Mineral X, 128 Units of Mineral Y, And 321 Units of mineral Z. The merchant needs to know how much he is paying per unit of mineral x, y, and z respectively, In order to stream line his operation.
He would also really appreciate an explaination and an equation ;)
Thanks so much!

Re: Word Problem
This is a difficult problem in that it dosen't have enough information for a reliable solution. For example, 500 units of Ore yields 321 units of X, 128 units of Y, and 321 units of Z. Its yields more units than it put in, 321+321+128 $\displaystyle > 500 $. Ok, Lets assume that the units for X,Y,Z are different units. This is a problem because we need to know the conversion between units if different units are being used, otherwise any analysis is useless.

Re: Word Problem
I dont know if this would help, but the average market value of 1 unit of mineral x is 172, Y is 14, and z is 6. Thanks for the effort anyway!

Re: Word Problem
1 unit of ore yields 321/500 of mineral X (assuming you always get the same amount each time you refine an ore), 128/500 of mineral Y, and 321/500 of mineral Z. it makes a difference if the game forces you to refine in batches of 500 (or other amounts) or lets you refine single ores (and also how the game handles "rounding").
assuming we put a value on the products of refinery solely based on the percentage of the whole they comprise, we get:
(321/770)*85 = 35.44 space bucks <a hefty profit, here
(128/770)*85 = 14.13 space bucks <just about breakeven
(321/770)*85 = 35.44 space bucks <losing money
overall, we turn a profit on every ore refined (not counting the cost of refining itself, which you give no information on), as the value of the product of one ore is:
0.642 * 174 ~ 110
0.256 * 14 ~ 3
0.642 * 6 ~ 3 (i am rounding down) = 116 space bucks on our investment of 85.
this is a very "crude" picture, as i have no idea if you receive all 3 minerals in the same proportion from every ore, or if its a choice of X,Y or Z (if it is, you should aim for X every time). if you CAN choose, it's a totally different kind of analysis.
if you are using these minerals to craft other items, you should obtain mineral X from refining, purchase mineral Z (if you need more than what you have on hand) from the market, and it doesn't matter much which method you use to obtain mineral Y (although if it's a "package deal" refining will allow you to sell the mineral X at enough of a profit to more than offset unloading the mineral Z at a loss).

Re: Word Problem
Thank you very much!
Yes just fyi the game forces you to refine in batches of 500 (for this particular ore) and 500 ores always yields the above amount of all three xyandz.
This game is a fantastic business/market simulator if your interested in that sort of thing. Its Called Eve Online.
Namaste!
Parker