Answer: The correct answer is D). Between 150 and 200; exclusive
Step-by-step explanation:
Given profit function p(x) of a tour operator is modeled by
p(x)=[tex](-2)x^{2} +700x-10000[/tex]
Where, x is the average number of tours he arranges per day.
To find number of tours to arrange per day to get monthly profit of at least 50,000$:
Now, he should make at-least 50000$ profit.
we can write as p(x)>50000$
[tex](-2)x^{2} +700x-10000\geq50000[/tex]
[tex](-2)x^{2} +700x-60000\geq0[/tex]
Roots are x is 150 and 200
(x-150)(x-200)>0
Case 1 : x>150 and x>200
x>150 also satisfy the x>200.
Case2: x<100 and x<200
x<200 also satisfy the x<100
Thus, the common range is 150<x<200
The correct answer is D). Between 150 and 200; exclusive
