Question 15
Find the maximum value of
$$
(1-x)(2-y)(3-z)\left(x+\frac{y}{2}+\frac{z}{3}\right)
$$
where $x\lt 1$, $y\lt 2$, $z\lt 3$, and $x+\frac{y}{2}+\frac{z}{3}\gt 0$.
$$
(1-x)(2-y)(3-z)\left(x+\frac{y}{2}+\frac{z}{3}\right)
$$
where $x\lt 1$, $y\lt 2$, $z\lt 3$, and $x+\frac{y}{2}+\frac{z}{3}\gt 0$.