Use quadratic functions. Suppose that the equation p(x) = -2x^{2}



Answered question


Use quadratic functions. Suppose that the equation p(x)=2x2+280x1000, 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?

Answer & Explanation

Michele Tipton

Michele Tipton

Beginner2021-11-30Added 11 answers

Step 1
We have,
1) p(x)=2x2+280x1000
This is a quadratic function with a=2, b=280 and c=1000×=b2a
Since a=2<0, which create open downward parabola because 'a' is negative which therefore, creates a maximum at the vertex.
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) x=b2a
Substitute the value of a=2 and b=280 in equation (2), we get
Therefore, the value of x-coordinates is 70
Hence, the number of items that maximize the profit is 70 items.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?