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P = − x 2 + 150 x − 4400 p = - x 2 + 150 x - 4400 is a profit formula for a small business. Find the set of x x -values that will keep this profit positive. Answer in interval notation.

1 Answer

1 vote

Answer:


x \in (40,110)

Explanation:

We are given the following in the question:


p(x)=-x ^2 + 150 x - 4400

where p gives the profit.

We want to keep the profit positive, thus


p(x)=-x ^2 + 150 x - 4400 > 0\\-x ^2 + 150 x - 4400 > 0\\x^2-150x+4400<0\\x^2-110x-40x+4400<0\\(x-110)(x-40)<0\\x<110,x<40\\x \in (40,110)

Thus, x should lie between 40 and 110 so that the profit is always positive.

User Katsharp
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