Question

many elevators have a capacity of 3000 pounds. complete parts (a) through (c) below. number of adults cause the elevator to be overloaded. the inequality is 60x + 100y > 3000. 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 $60x + 100y>3000$ for $y$. Subtract $60x$ from both sides: $100y>-60x + 3000$. Then divide by 100: $y>-\frac{60}{100}x+30$, or $y > - 0.6x + 30$.

Step2: Find the x - intercept

Set $y = 0$ in the equation $y=-0.6x + 30$. Then $0=-0.6x + 30$. Add $0.6x$ to both sides: $0.6x=30$. Solve for $x$: $x = 50$. So the x - intercept is $(50,0)$.

Step3: Find the y - intercept

Set $x = 0$ in the equation $y=-0.6x + 30$. Then $y=30$. So the y - intercept is $(0,30)$.

Step4: Graph the boundary line

The boundary line is $y=-0.6x + 30$. Since the inequality is $y > - 0.6x + 30$, the boundary line is dashed.

Step5: Shade the solution region

Choose a test point not on the line, say $(0,0)$. Substitute into the inequality: $0>-0.6(0)+30$ gives $0>30$ which is false. So shade the region above the line in the first quadrant.

Answer:

Graph a dashed line $y=-0.6x + 30$ with x - intercept $(50,0)$ and y - intercept $(0,30)$ and shade the region above the line in the first quadrant.