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how to tell if this constraints is dashed line or solid?
there is an example saying that:
John works between 10 and 30 hours per week at a restaurant. he earns $6.50 an hour, but he can earn tips when he delivers pizzas?
I understand the inequalities but why the inequality here as 10 ≤ t ≤ 30 is solid? it should be as 10 < t < 30.
I am understanding that if we have two dimensions, we make it as a solid, but if it is one dimension, it is open or dashed. can someone agree or correct?
here is a web link that talks about this:
http://www.mathsisfun.com/sets/intervals.html
i am still confused? thank you all. and till looking for help :).
2 Answers
- ?Lv 79 years agoFavorite Answer
It is a matter of whether you take the English literally or colloquially.
Strictly speaking you are correct: 10 < t < 30 is between.
However for sloppy English, "between" might mean "from 10 to 30 hours."
In the end, you will find intersections with the boundary lines anyway to get feasible , so no harm in including those boundary lines. If the feasible solutions do not land on the boundary lines, then the point is moot.
I understand that for textbook problems, this niggling detail can be annoying. In real applications we do not worry about them unless there is some really good, non-artificial reason for not including the boundary.
I hope these thoughts are helpful.
- 9 years ago
According to the example, he can also work 10 hours or 30 hours so they must be included in the inequality.
