I’m trying to prove that $F=0.15w+0.5x+0.15y+0.2z$ is greater than or equal to $G=0.25w+0.25x+0.25y+0.25z$. I also know some additional information:
$w\ge x\ge y\ge z$
$x=0.6w+0.4z$
$y=0.2w+0.8z$
So far, using some substitution, I’ve managed to work the problem down to this: $F=0.48w+0.52z$ and $G=0.45w+0.55z$. This is where I am stuck. I’m not sure how to prove $F\ge G$ from here. Any help would be appreciated, and links to resources where I could learn more about how to solve this particular problem are encouraged. Thanks!
Based on what you've already done, $F-G=0.03(w-z)$, which is non-negative because $w \geq z$.