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A deli owner has determined that his revenue, y, from selling sandwiches each day is at most -0.05r2 + 6x where x represents the number
of sandwiches he sells. To make a gprofit, his revenue must be greater than his costs, represented by the expression 1.5x + 45.
Write a system of inequalities to represent the values of x and ywhere the deli owner makes a profit. Then complete the statements.
The point (30,90) is
The point (60,160) is
of this system.
of this system.

Sagot :

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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.

How to get the system of inequalities?

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:

https://brainly.com/question/9774970

Answer:

30,90= not a solution
60,160= a viable solution

Step-by-step explanation:

View image Rynn0024
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