Question

The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = - 4x +2,400x - 400. Find the number of pretzels that must be sold to maximize profit.
O A. 359,600 pretzels

OB. 300 pretzels

OC. 600 pretzels

Answer 1

We have been given that the profit that the vendor makes per day by selling x pretzels is given by the function $P(x)=-4x^2+2400x-400$. We are asked to find the number of pretzels that must be sold to maximize profit.

First of all, we will find the derivative of our given function.

$P'(x)=-4\cdot 2x^{2-1}+2400$

$P'(x)=-8x+2400$

Now, we will find the critical point by equating derivative with 0 as:

$-8x+2400=0$

$-8x+2400-2400=0-2400$

$-8x=-2400$

$\frac{-8x}{-8}=\frac{-2400}{-8}$

$x=300$

Therefore, the company must sell 300 pretzels to maximize profit and option B is the correct choice.