Questions: Graph the inequality subject to the nonnegative restrictions. 16x - 40y > 1600, x ≥ 0, y ≥ 0 Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints.

Solution Steps

To graph the inequality $16x - 40y > 1600$, first rewrite it as an equation: $16x - 40y = 1600$.

To find the x-intercept, set $y = 0$ and solve for $x$: $16x - 40(0) = 1600$ $16x = 1600$ $x = 100$

To find the y-intercept, set $x = 0$ and solve for $y$: $16(0) - 40y = 1600$ $-40y = 1600$ $y = -40$

Plot the x-intercept $(100, 0)$ and the y-intercept $(0, -40)$ on the coordinate plane. Since the inequality is a strict inequality ($>$), draw a dashed line through these points.

Choose a test point not on the line, such as $(0,0)$. Plug the coordinates into the original inequality: $16(0) - 40(0) > 1600$ $0 > 1600$ Since this statement is false, shade the region that does _not_ contain the test point $(0,0)$.

The nonnegative restrictions $x \ge 0$ and $y \ge 0$ indicate that the solution must be in the first quadrant. So, only shade the portion of the region from Step 4 that is also in the first quadrant.

Final Answer: The solution is the region above the dashed line $16x - 40y = 1600$ and in the first quadrant.