What Quantities of Items $1, 2, 3$ combine to create an $X, Y, Z$ Target? Looking for the method.
$X$ Target: $1000$ | $Y$ Target: $500$ | $Z$ Target: $500$
Item $1$ contains:- $1.8 X | 2.1 Y | 2.0 Z$
Item $2$ contains:- $8.8 X | 1.9 Y | 1.7 Z$
Item $3$ contains:- $1.7 X | 2.0 Y | 7.4 Z$
Spent $8$ months trying to figure this out; please anyone that can help me. Many thanks.
Let there be $a$ of item $1$, $b$ of item $2$, and $c$ of item $3$. Then you have three equations, one each for the $X,Y,Z$ targets. Your equations are $$1.8a+8.8b+1.7c=1000\\2.1a+1.9b+2.0c=500\\1.7a+2.0b+4.7c=500$$ You can rewrite the first as $a=\frac{1000-8.8b-1.7c}{1.8}$ and plug this into the last two, then do the same to eliminate a variable from one, getting a linear equation in the last variable.
Alpha gives a solution $$a\approx 147.911\\ b\approx 79.719\\ c\approx 18.9602$$