The constraint is $3x + 2y \leq 90$ with $x \geq 0$ and $y \geq 0$.

Find the intercepts of the boundary line $3x + 2y = 90$:

• $x$-intercept: set $y = 0$ $\Rightarrow$ $3x = 90$ $\Rightarrow$ $x = 30$, giving point $(30, 0)$
• $y$-intercept: set $x = 0$ $\Rightarrow$ $2y = 90$ $\Rightarrow$ $y = 45$, giving point $(0, 45)$

The inequality $3x + 2y \leq 90$ represents the region on or below the line, in the first quadrant. The correct graph shows the shaded region below the line connecting $(30, 0)$ and $(0, 45)$.