Question

many elevators have a capacity of 3500 pounds. complete parts (a) through (c) below. number of adults cause the elevator to be overloaded. the inequality is 50x + 140y > 3500. 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 inequality for graphing

First, rewrite $50x + 140y>3500$ in slope - intercept form $y=mx + b$. Solve for $y$:
\[

$$\begin{align*} 50x+140y&>3500\\ 140y&>- 50x + 3500\\ y&>-\frac{50}{140}x+\frac{3500}{140}\\ y&>-\frac{5}{14}x + 25 \end{align*}$$

\]

Step2: Find the boundary - line points

The boundary line is $y =-\frac{5}{14}x + 25$. When $x = 0$, $y=25$ (the $y$ - intercept). When $y = 0$, we solve $0=-\frac{5}{14}x + 25$ for $x$.
\[

$$\begin{align*} \frac{5}{14}x&=25\\ x&=25\times\frac{14}{5}\\ x&=70 \end{align*}$$

\]

Step3: Graph the boundary - line and shade

Graph the points $(0,25)$ and $(70,0)$ and draw a dashed line (since the inequality is $>$ not $\geq$) through them. Then, since $y>-\frac{5}{14}x + 25$, shade the region above the line in the first quadrant (because $x\geq0$ and $y\geq0$).

Answer:

Graph a dashed line passing through $(0,25)$ and $(70,0)$ and shade the region above the line in the first quadrant.