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 70x + 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 the inequality in slope - intercept form

First, solve $70x + 140y>3500$ for $y$. Subtract $70x$ from both sides: $140y>-70x + 3500$. Then divide by 140: $y>-\frac{1}{2}x + 25$.

Step2: Find the boundary line

The boundary line of the inequality $y>-\frac{1}{2}x + 25$ is $y =-\frac{1}{2}x+25$. Since the inequality is $>$, the boundary line will be dashed.

Step3: Find the x - intercept

Set $y = 0$ in $y=-\frac{1}{2}x + 25$. Then $0=-\frac{1}{2}x+25$, $\frac{1}{2}x=25$, and $x = 50$. So the x - intercept is $(50,0)$.

Step4: Find the y - intercept

Set $x = 0$ in $y=-\frac{1}{2}x + 25$. Then $y=25$. So the y - intercept is $(0,25)$.

Step5: Graph the inequality

Plot the x - intercept $(50,0)$ and y - intercept $(0,25)$ and draw a dashed line through them. Since $y>-\frac{1}{2}x + 25$, shade the region above the line in the first quadrant (because $x\geq0$ and $y\geq0$).

Answer:

Graph a dashed line with x - intercept $(50,0)$ and y - intercept $(0,25)$ and shade the region above the line in the first quadrant.