Question

many elevators have a capacity of 4000 pounds. complete parts (a) through (c) below. number of adults cause the elevator to be overloaded. the inequality is 40x + 160y > 4000. b. graph the inequality. because x and y must be positive, limit the graph to quadrant i only. use the graphing tool to graph the inequality.

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, rewrite $40x + 160y>4000$. Subtract $40x$ from both sides: $160y>-40x + 4000$. Then divide each term by 160: $y>-\frac{40}{160}x+\frac{4000}{160}$, which simplifies to $y>-\frac{1}{4}x + 25$.

Step2: Find the boundary - line points

The boundary line of the inequality $y =-\frac{1}{4}x + 25$ is a straight line. When $x = 0$, $y=25$ (the y - intercept). When $y = 0$, we solve $0=-\frac{1}{4}x + 25$. Add $\frac{1}{4}x$ to both sides: $\frac{1}{4}x=25$, and then multiply both sides by 4 to get $x = 100$ (the x - intercept).

Step3: Graph the boundary line and shade the region

Draw a dashed line (since the inequality is $>$ not $\geq$) through the points $(0,25)$ and $(100,0)$. Since $y>-\frac{1}{4}x + 25$, we shade the region above the line in the first quadrant (because $x\geq0$ and $y\geq0$).

Answer:

Graph a dashed line through $(0,25)$ and $(100,0)$ and shade the region above the line in the first quadrant.