Ashifur September 9, 2023 - 17:55
Problem: The profit of a company in Taka is given by P = $3x^{2}$ – 35x + 50, where x is the amount in Taka in lac spent on advertising. For what values of x does the company make a profit?

View all: RUPALI BANK LTD (CANCELLED) WRITTEN QUESTION (MATH) SOLVE | 2018

Correct Answer: 0$\lt$ x$\le$$\frac{5}{3}$

Explanation:

Here. p = 3x$^{2}$-35x + 50Now. if the company makes a profit. thenP > 0

=> 3x$^{2}$ – 35x + 50> 0

=> 3x$^{2}$ -30x – 5x + 50 > o

=> 3x(x-10) – 5(x-10) > 0

so, (x-10)(3x-5) > 0 ………….(i)AS this equation (i) is greater than 0, so the value of the two roots must have different intervals.

Now, from the equation (i). We have, The value of x is greater than 10 L.e. x > 10

Or, the value of x is less than $\frac{5}{3}$ and greater than or equal to 0 i.e.0$\lt$ x$\le$$\frac{5}{3}$ because advertising cost can not be negative.

So. if the company makes a profit. the values of x=0$\le x\lt \frac{5}{3}or,x\gt$10

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