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

Question

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.

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Sophia 1 week 2021-11-23T19:57:08+00:00 1 Answer 0 views 0

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    2021-11-23T19:58:46+00:00

    Answer:

    x \in (40,110)

    Step-by-step 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.

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