Use quadratic functions. Suppose that the equation p(x)=−2x2+280x−1000, where x represents the number of items...



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.

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