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

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Michele Tipton · Accepted Answer

Step 1 We have, 1) p(x)=−2x2+280x−1000 This is a quadratic function with a=−2, b=280 and c=−1000×=−b2a Since a=−2&amp;lt;0, which create open downward parabola because &#039;a&#039; 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 ⇒x=−2802×(−2) ⇒x=−280(−4) ⇒x=2804 ⇒x=70 Therefore, the value of x-coordinates is 70 Hence, the number of items that maximize the profit is 70 items.

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

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