please help me please

Question

The profit function p(x) of a tour operator is modeled by p(x) = −2x² + 700x − 10000, 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?

A.) more than 200

B.) less than 150

C.) between 150 and 200; exclusive

D.) between 150 and 200; inclusive

Please include and only include the explanation and the solution.

Answer 1

50000 ≤ -2x² + 700x - 10000

0 ≤ -2x² + 700x - 60000

0 ≥ x² - 350x + 30000

0 ≥ (x - 200)(x - 150)

150 ≤ x ≤ 200