The profit that the vendor makes per day by selling x pretzels is given by the function P(x)=−4x2+2,800x−350. Find the number of pretzels that must be sold to maximize profit.

Answer 1

Hi Gabriela F

If

P(x) = -4x² + 2800x - 350

is your equation then

a = -4

b = 2800

c = 350

Since a is negative your parabola opens downward, so the vertex represents the maximum of your curve.

You need only to find the vertex of your parabola which can be calculated as follows:

The x coordinate of the vertex is

x = -b/2a

Once x is found then you just plug that into to your equation above to find P(x)

I got (350, 489,650) as the vertex.

I hope that helps

You can also graph your parabola at Desmos.com

Answer 2

P(x) is a quadratic equation, so its graph is a parabola. Since the leading coefficient is negative (-4), the parabola is inverted with the vertex at the top, so the vertex is the maximum profit point. The x-coordinate of the vertex is given by:

x = -b/2a

where b = 2800 and a = -4. Plug in the numbers to get the answer. The units are pretzels.