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2021-11-29

Use quadratic functions. Suppose that the equation $p\left(x\right)=-2{x}^{2}+280x-1000$ , where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

Michele Tipton

Beginner2021-11-30Added 11 answers

Step 1

We have,

1)

This is a quadratic function with

Since

Let us determine the number of terms that should be produced to maximize the cost by find the x-value of the vertex.

We know that, vertex of parabola be:

2)

Substitute the value of

Therefore, the value of x-coordinates is 70

Hence, the number of items that maximize the profit is 70 items.

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