What is the maximum weight that can be carried by the elevator?
B
b
Consider the results in Part A.
A
a
Inequality: 75x+40y≤ 1800
Graph:
B
b
See solution.
Practice makes perfect
a
We want to write and graph an inequality for the given situation. Let's recall the given information.
Large Boxes:& 75 lb
Small Boxes:& 40 lb
Delivery Person:& 200 lb
Weight Limit:& 2000 lb
Let x be the number of large boxes and let y be the number of small boxes. By using the given information, we will first write an inequality in an organized table.
Therefore, we have an inequality that represents the situation. Let's simplify it by isolating the variables on the left-hand side.
75x+40y+200 ≤ 2000
⇕
75x+40y ≤ 1800
To graph it, we will first determine the boundary line of the inequality by replacing the inequality sign with the equals sign.
Inequality &Boundary Line
75x+40y ≤ 1800 &75x+40y = 1800
Now, we will draw the boundary line. Since the equation of the line is in standard form, we can draw it by finding its intercepts. To find the x-intercept, we will substitute y=0 in the equation and solve it for x. We will proceed in the same way to find the y-intercept as well.
x-intercept
y-intercept
Substitution
Point
Substitution
Point
75x+40( 0)=1800
(24,0)
75( 0)+40y = 1800
(0,45)
Next, we will plot the intercepts and draw the boundary line that passes through these points. Note that the number of boxes cannot be negative, so the line will be restricted by the axes. Additionally, since the inequality is non-strict, the line will be solid.
Finally, we will decide which side of the line we should shade. We will choose a point at either side of the line and substitute it into the inequality. If it satisfies the inequality, we shade the region that contains the point. Otherwise, we shade the other region. Let (0,0) be our test point!
There can be more than one reason why some solutions of the inequality might not be practical in real life. One of them can be that the number of the boxes must be positivewhole numbers. Besides, a delivery person cannot take 10.5 large boxes and 20.5 small boxes.
