Correct Answer: ${0\le x\lt \frac{5}{3}} or, x\gt 10$

Explanation:

Here, p = 3x$^{2}$-35x+50

Now. if the company makes a profit

p >0=> 35$^{2}$ + 50 > o

=> 3x$^{2}$ -30x – 5x + 50 > 0

=> 3x(x- IO) – 5(x – l0) >0………………………………….(i)

As this equation (i) is greater than 0. so the value of the two roots must have different values in different intervals.

Now . front the equation (i), we have, The value of x is greater than 10  . So x > 10

0r. the value of x is less than $\frac{5}{3}$ and greater tlum or equal to 0 i.e. 0 $\le x\lt \frac{5}{3}$

because advertising cost can not be negative.

So. if the company makes a prof it. the values of x  is