A firm makes x batches of product P and y batches of product Q…

Step 1. The machine lines. From $2x + y = 40$ we get $y = 40 - 2x$. Then $x + 3(40 - 2x) = 75$ gives $-5x = -45$, so $x = 9$ and $y = 22$.

Step 2. The values at the corners. The corners are $(0, 0)$, $(20, 0)$, $(9, 22)$ and $(0, 25)$. $Z$ is $0$, $140$, $63 + 198 = 261$ and $225$. The maximum is $261$ at $(9, 22)$.

Step 3. The storage rule. At $(9, 22)$, $x + y = 31$, which is below $35$. The storage line never touches the region, so the rule is redundant.