The finale of these unoriginal problems, yay!

I don't create this problem. All of the credits go to Nguyễn Tất Thu, Đoàn Quốc Việt and Vũ Công Minh for writing these problems, and the books in general.

This is two problems combined into one, from two different books.

$a$ , $b$ , $c$ , $x$ , $y$ , $z$ are real numbers such that $a$ and $b$ are non-negatives and

$\large \left\{ \begin{aligned} 5(4c - 3a - 2b) = 3b + 7c - 2a &= 20\\ yz + zx + 3x + y = yz + 2zx + 5x &= 1\\ \end{aligned} \right.$

Let $M = 2c^2 + a^2 + 3ab + 4bc$ and $N = xy(z + 2)$ .

Calculate the value of the following expression.

$\large \text{(MinM + MaxN)(MaxM + MinN) + (MaxN + MinN)}$