The profit function p(x) of a tour operator is modeled by p(x) = −2x^2 + 700x − 1, where x is the average number of tours he arranges per day. what is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $50,000?

Range of the average number of tours is between 150 and 200 including 150 and 200.

Step-by-step explanation:

Given:

The profit function is modeled as:

The profit is at least $50,000.

So, as per question:

Now, rewriting the above inequality in terms of its factors, we get:

Now,

Therefore, the range of the average number of tours he must arrange per day to earn a monthly profit of at least $50,000 is between 150 and 200 including 150 and 200.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1