The system of inequalities is:
y ≤ -0.05*x^2 + 6x
y > 1.5x + 45
(30, 90) is not a solution of that system, while (60, 160) is a solution.
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How to get the system of inequalities?</h3>
We know that the revenue y is given by:
y ≤ -0.05x^2 + 6x
And we know that the costs are 1.5x + 45, and the revenue must be larger than that, so we also have the inequality:
y > 1.5x + 45
So the system is:
y ≤ -0.05*x^2 + 6x
y > 1.5x + 45
Now, the point (30, 90) means that we need to replace x by 30 and y by 90, replacing that in the second inequality, we will get:
90 > 1.5*30 + 45 = 90
90 > 90
This is false, so the point is not a solution of this inequality, meaning that the point is not a solution of the system.
For the second point we do the same: x= 60, y = 160, replacing that in the second inequality we get:
160 > 1.5*60 + 45 = 135
160 > 135
This is true, now we need to check with the other inequality.
160 ≤ -0.05*60^2 + 6*60 = 180
This is also true.
So the point (60, 160) is a solution to the system.
If you want to learn more about systems of inequalities, you can read:
brainly.com/question/9774970
