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A sales team estimates that the number of new phones they will sell is a function of the price that they set. They estimate that if they set the price at x dollars, they will sell f(x)=1220−5x phones. Therefore, the company's revenue is x⋅(1220−5x). Find the price x which will maximize the company's revenue.

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TaeKwonDoIsDead

Answer:

$122

Step-by-step explanation:

If we want the maximized value, we need to differentiate the function and set it equal to 0, then solve for x.

We want to maximize revenues, so we call the revenue function r(x) and differentiate, equate to 0, and solve:

[tex]r(x)=x(1220-5x)\\r(x)=1220x-5x^2\\r'(x)=1220-10x\\0=1220-10x\\10x=1220\\x=122[/tex]

Thus, $122 will maximize the revenue.

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