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

`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.