$$\left. \begin{array} { l } { A = 20 \% x + 80 \% y } \\ { B = 70 \% x + 30 \% y } \\ { x + 50 x + 30 \% y y \right.$$
$z=\frac{3\left(7A-2B\right)^{2}}{250}+\frac{408B}{5}-\frac{153A}{5}$
$$100A=20x+80y$$ $$100B=70x+30y$$ $$100z=5100x+30y^{2}$$
$$x=5A-4y$$
$$100B=70\left(5A-4y\right)+30y$$ $$100z=5100\left(5A-4y\right)+30y^{2}$$
$$y=-\frac{2}{5}B+\frac{7}{5}A$$ $$z=\frac{3}{10}y^{2}-204y+255A$$
$$z=\frac{3}{10}\left(-\frac{2}{5}B+\frac{7}{5}A\right)^{2}-204\left(-\frac{2}{5}B+\frac{7}{5}A\right)+255A$$
$$z=-\frac{153}{5}A+\frac{408}{5}B+\frac{3}{250}\left(-2B+7A\right)^{2}$$
$$x=5A-4\left(-\frac{2}{5}B+\frac{7}{5}A\right)$$
$$x=-\frac{3}{5}A+\frac{8}{5}B$$
$$x=-\frac{3}{5}A+\frac{8}{5}B$$ $$y=-\frac{2}{5}B+\frac{7}{5}A$$ $$z=-\frac{153}{5}A+\frac{408}{5}B+\frac{3}{250}\left(-2B+7A\right)^{2}$$
Show Solution
Hide Solution
