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.

Answer 1

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

$p(x)=-x ^2 + 150 x - 4400 > 0\\-x ^2 + 150 x - 4400 > 0\\x^2-150x+4400$

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