solve the following mathematical problems:

The profit of a company is given in taka by p= $3 x^{2} - 35 x + 50$ , where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

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

Now, if the company makes a profit, then

$p > 0 \Rightarrow 3 x^{2} - 35 x + 50 > 0 \Rightarrow 3 x^{2} - 30 x - 5 x + 50 > 0 \Rightarrow 3 x (x - 10) - 5 (x - 10) > 0 \Rightarrow (x - 10) (3 x - 5) > 0 . . . . . . . . . . . . . . . (i)$

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

Now, from the equation (i), we have

The value of x is greater than 10 ie: x> 10

Or, the value of x is less than $\frac{5}{3}$ and greater than or equal to 0 i.e. $0 \leq x < \frac{5}{3}$

Because advertising cost can not be negative.

So, if the company makes a profit,

The values of $x = \{0 \leq x \leq \frac{5}{3} o r, x > 10\}$ .

1 year ago

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The profit of a company is given in taka by p= $3 x^{2} - 35 x + 50$ , where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?

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The profit of a company is given in taka by p= 3x2-35x+50, where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?

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The profit of a company is given in taka by p= $3 x^{2} - 35 x + 50$ , where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?