The profit that the vendor makes per day by selling x pretzels is given by the function Upper P (x )equals negative 4 x squared plus 2 comma 400 x minus 400. Find the number of pretzels that must be sold to maximize profit.

The number of pretzels that must be sold to maximize profit is 300.

Step-by-step explanation:

The daily profit of selling x pretzels is given by the following equation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is

Find the number of pretzels that must be sold to maximize profit.

This is the x of the vertex.

We have that:

So

Then

The number of pretzels that must be sold to maximize profit is 300.

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step-by-step explanation: