Transportation An air cargo plane can transport as many as 15 regular shipping containers. One super-size container takes up the space of 3 regular containers.
Write an inequality to model the number of regular and super size containers the plane can transport.
Describe the domain and range.
Graph the inequality you wrote in part (a).
This is an example of how it should be answered:
Answers may vary. Sample: x+3y≤15
x plus 3 y less than or equal to 15
b. Answers may vary. Sample: domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, range: {0, 1, 2, 3, 4, 5}
c. A graph of a solid line segment falls from (0, 5) to (15, 0). The region below the line is shaded. All values are approximate.
a. Let x represent the number of regular shipping containers and y represent the number of super-size containers.
Since one super-size container takes up the space of 3 regular containers, the total number of containers the plane can transport can be represented by the inequality:
x + 3y ≤ 15
b. The domain represents the possible values for x and y. In this case, x and y can be any non-negative integers since it is natural to consider whole numbers of containers.
Therefore, the domain is:
{x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
{y: 0, 1, 2, 3, 4, 5}
The range represents the possible number of regular and super-size containers that can be transported. Since the inequality states that the number of regular and super-size containers combined must be less than or equal to 15, the range is the same as the domain for both x and y.
Therefore, the range is:
{0, 1, 2, 3, 4, 5}
c. To graph the inequality x + 3y ≤ 15, we can create a graph with x on the horizontal axis and y on the vertical axis. Since x and y both represent the number of containers, we can mark the points on the graph using the domain and range values.
A solid line segment falls from (0, 5) to (15, 0). This line represents the boundary of the shaded region, which consists of all the points below the line. All values on and below the line represent valid solutions for the inequality.
The graph should look something like this: (Note: The graph is not drawn to scale)
|
5 | _
| _,-'
4 | _,-'
| _,-'
3 |,-'
|'
2 |
|
1 |
|
0 |________________________________
0 1 2 3 4 5 6 7 8
The shaded region will be below the line segment.